In Memoriam C Kanellakis

Our colleague and dear friend Paris C Kanellakis died unexp ectedly and tragically on De

cemb er together with his wife MariaTeresa Otoya and their b eloved young children

Alexandra and Stephanos En route to Cali Colombia for an annual holiday reunion with his

wifes family their airplane strayed o course without warning during the night minutes b efore

an exp ected landing and crashed in the Andes

As researchers we mourn the passing of a creative and thoughtful colleague who was resp ected

for his manycontributions b oth technical and professional to the research

community As individuals wegrieveover our tragic lossof a friend who was regarded with great

aection and of a happy thriving family whose warmth and hospitalitywere gifts appreciated

by friends around the world Their deaths create for us a void that cannot b e lled

Paris left unnished several pro jects including a pap er on theory intended for this

sp ecial issue of Computing Surveys to b e written during his holiday visit to Colombia Instead

we wish to oer here a brief biographyofParis and a description of the research topics that

interested Paris over the last few years together with the contributions that he made to these

areas It is not our intention to outline denitive surveys or histories of these areas but rather

to honor the signicantcontemp orary research of our friend

Paris was b orn in in to Eleftherios and Argyroula Kanellakis In he received

the Diploma in from the National Technical UniversityofAthens his

al undergraduate thesis was titled Easytotest Criteria for Weak Stochastic Stability of Dynamic

Systems advised by Prof E N Protonotarios Paris continued his studies at the graduate level in

Electrical Engineering and Computer Science at the Massachusetts Institute of Technology where

he received his M Sc in submitting the thesis Algorithms for a Scheduling Application of

the Asymmetric Traveling Salesman Problem sup ervised by Profs R Rivest and M Athans

followed by his Ph D in his do ctoral dissertation was On the Complexity of Concurrency

Control for Distributed sup ervised by Prof C H Papadimitriou

In Paris joined the Computer Science Department of as assistant

professor He was promoted to asso ciate professor with tenure in and to full professor in

Intermittent with his app ointment at Brown Paris also held several temp orary p ositions

including p osts at the IBM Watson ResearchCenter the MIT Lab oratory for Computer Science

GIP Altar and INRIA Ro cquencourt He served as an asso ciate editor of the new journal

Constraintsaswell as Information and Computation ACM Transactions on Database Systems

SIAM Journal of Computing Theoretical Computer Scienceand Journal of Logic Programming

vited sp eaker at Paris served in addition as program committee memb er program chair and in

many of the prominent research conferences in computer science

We take this opp ortunity to presentsomeofParis contributions to database theory includ

ing deductive ob jectoriented and constraint databases as well as his work in faulttolerant

distributed computation and in typ e theoryIneach of these areas we recognize research contri

butions that were not merely examples of go o d problem solving but also examples of insightful

problem formulation

In synchrony with his technical ability in solving problems Paris added a mature editorial

voice which by prop osing new kinds of research questions and answering some of them in novel

and sometimes surprising ways help ed to change our p erceptions of what was technically sig

nicant In several casesfor example in deductive databases and typ e theoryParis brought

the to ols and techniques of complexity theory and algorithmics to analyze the eciency of con

structs in programming language design These themes were found again in the area of constraint

databases an area he played a ma jor role in initiating while guiding its development via sound

and feasible algorithmic principles In Paris advanced new computational

frameworks intended to align algorithmic paradigms with salient asp ects of realizable system

architectures In ob jectoriented databases Paris worked to build a semantic foundation that

provides an implementationindep ende nt meaning for these systems much in the same spirit that

the relational mo del provides an implementationindep ende nt meaning for relational databases

We recognize in all this work Paris desire to understand b etter the theoretical foundations of

practical systems to study them with precise analytical to ols and to use the results to improve

the functionality and p erformance of these systems

The authors of this technical obituary feel honored by the privilege they had in collab orating

with Paris on many of these pro jects In mourning his tragic death we miss his technical facility

his broad knowledge his insight his commitment and his humor To write a research pap er with

Paris was also an opp ortunity to observe his indefatigable attention to detail and to engage in

vigorous debate with his editorial voice To write this obituary allowed us to to feel his voice

tist he was and to appreciate his uncommon once more to understand b etter what a go o d scien

decency and kindness It is our great loss that we will not hear his voice again

Deductive Databases

Paris Kanellakis was a ma jor contributor to the theoretical foundations of deductive databases

It has b een recognized since the early s that rstorder database query languages suchas

SQL are lacking in expressivepower This insight lead to the investigation of many higherorder

query languages in particular Datalog the language of logic programs without function symb ols

A canonical use of Datalog is to compute transitiveclosurewherewe think of the database as a

directed graph

pathX Y edge X Y

pathX Y pathX Z pathZ Y

In this example wetake edge to b e an extensional database EDB predicate representing

basic facts stored in the database For example edge is an EDB fact stating that there is

an edge b etween vertices and The intensional database IDB predicate path represents facts

deduced from the database via the logic program ab ove the rst rule says every directed edge

forms a path and the second rule tells how paths can b e joined together We can now query for

instance path or pathV to determine resp ectively whether there is a path from vertex

tovertex or what vertices V are connected to vertex by a path The path facts are deduced

from the edge facts hence the name deductive databases

Paris work addressed the problem of nding ecientevaluation metho ds for Datalog queries

He viewed the challenge of deductive databases as the need to combine the technology of logic

programming with the eciency of database technology providing a concrete step towards a

new generation of computing The fo cus of his research in this area was in identifying classes of

Datalog queries that can b e evaluated eciently

Datalog and Parallel Computation Paris investigated what kind of Datalog queries can

b e sp edup by massive parallelism CK Kan He identied sp eedup with the complexity

class NC which consists of the problems that can b e computed in p olylogarithmic time through

the use of p olynomially b ounded hardware Problems in NC are exactly those with a great

deal of p otential parallelism In contrast signicant sp eedups cannot b e achieved for PTIME

complete problems unless NCPTIME which is widely b elieved not to b e the case Thus

PTIMEcomplete problems are often called inherently sequential

Paris prop osed to measure the computational complexity of Datalog programs b oth by their

time complexityaswell as by their database complexity which measures the numb er of calls the

Datalog query engine makes to the underlying relational database system He proved that there

are Datalog queries that are hard to evaluate in parallel regardless of which complexity measure

is b eing used For example Paris showed that the query

reachX reachY reachZ edge Y X edgeX Z edge Z Y

vably sup erp olylogarithmic is PTIMEcomplete and furthermore its database complexityispro

The latter b ound is signicant since it do es not dep end on whether NC is a prop er sub class of

PTIME Paris also proved a gap theorem for the databasecomplexity measure He showed that

the database complexityofevery Datalog query is either O orlogn surprisingly there is

nothing in b etween

Bounded vs Unb ounded Queries It is clear that recursive applications of Datalog rules

make queries hard to evaluate In particular Datalog queries whose database complexityisin

O can b e evaluated in NC such queries are called boundedItisknown that a Datalog query

is equivalent to a rstorder query i it is b ounded This makes it highly desirable to b e able

to identify which Datalog queries are b ounded Unfortunately the distinction b etween b ounded

and unb ounded queries can b e quite subtle For example the query

buys X Y likes X Y

buys X Y trendy X buys Z Y

is b ounded while the query

buys X Y likes X Y

buys X Y knows X Z buys Z Y

is unb ounded This subtlety is not accidental it is known that the problem of testing whether a

given Datalog query is b ounded or not is undecidable

Paris was engaged in a longterm pro ject whose goal was to delineate the b oundary b etween

the decidable and undecidable for classes of Datalog queries CGKVAK HKMV that

is to identify maximal classes of Datalog queries whose b oundedness problem is decidable and

minimal classes of Datalog queries whose b oundedness problem is undecidable

One way of classifying Datalog programs is bythearity of their IDB predicates For example

the path and buys queries in the examples ab ove are binary while the reach query is unary

Together with colleagues Paris was able to show that the b oundary b etween the decidable and

the undecidable lies b etween the unary and the binary More precisely the b oundedness problem

for unary Datalog queries is decidable CGKV while the b oundedness problem for binary

Datalog queries in undecidable HKMV

Ob jectOriented Databases

In Paris visited INRIA Ro cquencourt where he held a joint p osition in the Database

Research Group and in the Altar RD Group At that time ob jectoriented database systems

were emerging from researchvenues and into pro duct development with startup companies such

as Altar The new technologyhowever lacked the formal foundations of the relational mo del

Paris goal while participating in development eorts was to bridge this gap

While at Altar Paris had a ma jor inuence on several asp ects of the O system bringing his

theoretical exp ertise to a practical pro ject His most visible impact was on the data mo del he

help ed formulate the O data mo del and provided a nal theoretical framework for it He was

also the lead editor of the denitive monograph BDK do cumenting the relevant design and

analysis of this multiyear research and development eort

OneofParis ambitions was to provide sound theoretical foundations to database systems He

strongly b elieved that understanding the functionalities of these systems providing formal mo dels

for them and nding connections with already mature theories were the keystodeveloping b etter

systems In this enterprise Paris could rely on a wide culture in theoretical computer science

and mathematics as well as a strong intuition for practical issues

Paris develop ed an ob jectbased database mo del in a collab orativework AK AK The

structural part generalized most of the known complexob ject data mo dels The main contri

bution is the op erational part of the data mo del the query language IQL which uses ob ject

identities oids for three critical purp oses to represent datastructures with sharing and

cycles to manipulate sets and to express any computable database query The lan

ked can b e evaluated b ottomup and naturally generalizes guage IQL can b e statically typ e chec

most p opular rulebased database languages The mo del was also extended to incorp orate typ e

inheritance without changes to the language

The main purp ose of this work was to capture formally the essence of ob ject database applica

tion programming and to highlight the new dimension broughtby ob ject identity with regard to

old questions such as duplicate elimination or query completeness In particular Paris observed

that standard pro ofs of query completeness eg CH did not work as usual in this setting

b ecause of the presence of oids He showed that an analogous valuebased data mo del could b e

founded on regular innite trees thereby capturing fundamental asp ects of ob ject identity that

had b een overlo oked by previous researchers

Paris was also concerned with the essential novelty of programming applications in an ob ject

oriented paradigm In AKRWHKRheinvestigated with collab orators a simple program

ming formalism for ob jectoriented databases namely method schemas The syntax is based on

an application of program schemas using a hierarchy of classes metho d comp osition recursion

via function calls and name overloading The semantics is based on term rewriting with late

binding

Paris and colleagues concentrated on understanding the problem of consistency checking ie

of testing at compile time whether in some interpretation a metho d invocation would lead to an

error Not surprisingly the problem is undecidable in general Paris studied in depth decidable

cases such as monadic schemas metho ds having arity or recursionfree schemas absence of

cycles in the metho d dep endence graph Some surprising consequences of covariance a standard

restriction imp osed on metho d denitions were demonstrated for an imp ortant class of monadic

CE whereas it is complete recursionfree schemas consistency checking is complete for NLOGSPA

for DLOGSPACE if covariance is also imp osed

Paris was convinced that ob jectoriented databases were an imp ortanttechnological step

but that they needed to rely on previously develop ed theories and techniques He viewed his

more recentwork on typ e theory see Section as part of a general program to provide formal

foundations for database programming languages

Constraint Databases

Paris was one of the founders of the area of Constraint Databases KKR While visiting

the IBM T J Watson ResearchCenter he was shown a demonstration of the CLPR system

This system is an instance of the CLPX framework an extension of logic programming in

which rules contain b esides normal terms constraints from a domain X CLPR in which rules

contain constraints from the domain of real numb ers uses a combination of lazy evaluation and

an appropriate constraintsolver together with standard techniques from logic programming

Paris immediately wondered whether a database theory could b e develop ed for such systems by

analogy with the way deductive databases were inspired by logic programming

The direct consequence of this idea was his collab orativework on Constraint Query Languages

KKR A class of database mo dels and query languages was dened that could b e instantiated

by sp ecic constraint domains similar to the CLPX framework The basic idea was to replace

the notion of tuple in a relational database by that of a generalized tuple ie a conjunction

of constraints A relational tuple a a for example can b e regarded as a sp ecial case

n

of a generalized tuple ie x a  x a By cho osing more p owerful classes of

n n

constraints one can representpotentially innite sets of p oints in a compact wayFor example

a rectangle with corners at a b and c d can b e represented by the generalized tuple a  x 

b c  y  d Other example are linear arithmetic constraints which can b e used to mo del

many spatial applications eg GIS and p olynomial constraints which can b e used to describ e

more complex spatial ob jects such as those in CAD systems

Of course just extending the database mo del would b e not b e very interesting unless we

were able to query the database Paris realized that for the mo del to b e of interest wewould

need query languages that were not just decidable but of low complexity This researchgoalwas

addressed in KKR for denseorder constraints ie inequalities xy where is a dense order

eg the rationals Some results in this direction have also b een obtained for more p owerful

query classes such as linear constraints and p olynomial constraints

Paris original pap er showed that the rstorder query language with denseorder constraints

could b e evaluated in LOGSPACE Subsequent jointwork KG improved these b ounds to

as to resolve for denseorder constraints a problem that AC One consequence of this result w

Paris had prop osed for rstorder constraint query languages in general whether the PARITY

queryis the cardinality of a nite database even or o ddis expressible in such languages His

conjecture was that the answer is negative as is wellknown to b e the case for relational databases

This question turned out to b e a very dicult for p olynomial constraints the negative result

was only obtained recently BDLW using sophisticated techniques from nonstandard mo del

theory

The AC result referred to ab ovewas obtained by dening an algebra for denseorder con

straints and then analyzing its complexity In one of his very last pap ers GK Paris extended

this work and studied algebras for constraint databases in more detail This research included fur

ther work on denseorder constraints including up date issues and linear arithmetic constraints

In the latter case he dened a particularly promising algebra for variable constraintsfor

example temp oral constraints

OneofParis goals was to include recursion eg transitive closure in the mo del Unfortu

nately languages more p owerful than denseorder constraints were not closed under recursion

For example if Rx y contained the generalized tuple y x the transitive closure of R would

n

havetocontain all tuples of the form y xforn  On the other hand it was p ossible to

write recursive programs that did not have this problem intuitively by ensuring that the rules

one wrote did not create new ob jects Dening such a notion in a precise waywas an abiding

interest of Parisunfortunately it remained an uncompleted pro ject

Paris was always concerned ab out the practical side of the eld and was aware of the risk of

it b ecoming a theoretical exercise with limited practical value From the very b eginning he was

interested in the question of appropriate index structures for constraint databases ie howto

store constraints so that they could b e accessed ecientlyHespent an extended visit to IBM

studying the state of the art in index structures for spatial databases and how applicable they

were to constraints He was immediately struckby the contrast b etween the elegantcombination

of theory and practice in the original Btree pap er and the lackofsuch an analysis for spatial

index structures The result of this study was the pap er KRVV prop osing a data structure

for indexing constraints on one attribute This index structure has optimal worstcase storage

and query p erformance and optimal amortized insert time ie averaged overasequenceof

inserts with p erformance very close to that of the Btree By studying the techniques that

he had used for indexing constraints RK Paris was also able to develop index metho ds for

ob jectoriented databases and at the time of his death he was investigating their application to

temp oral databases

FaultTolerantParallel Computation

Paris Kanellakis among other researchers sought to bridge the gap b etween abstract mo dels of

parallel computation and realizable parallel architectures The parallel random access machine

pram mo del attracted signicant attention and numerous ecient parallel algorithms were

develop ed for the mo del The pram mo del elegantly combines the p ower of parallelism and the

simplicity of the random access machine ram mo del Most parallel algorithms require a fault

free environment where any unreliability of pro cessors interconnections or synchronizations

either eliminate eciency or result in incorrect computation Paris prop osed a formally dened

notion of robustness that combines faulttolerance and eciency and he led the development

of deterministic parallel algorithms that remain ecient in the presence of arbitrary dynamic

pro cessor failure patterns This work and relevantopenproblemswere recently summarized

in KMS KS

Robust computation The ultimate goal of this reasearch is the synergy b etween the speedup

p otential of parallel computation and the reliability p otential of distributed computation Paris

investigated fault mo dels and parallel computation mo dels where it is p ossible to achievealgo

rithmic eciency ie sp eedups close to linear in the numb er of pro cessors despite the presence

of faults Such combinations of fault and computation mo dels illustrate constructive tradeos

between reliability and eciency This tradeo exists b ecause reliability usually requires intro

ducing redundancy in the computation in order to detect errors and reassign resources whereas

gaining eciency by massively parallel computing requires removing redundancy from the compu

tation to fully utilize each pro cessor Even allowing for some abstraction in the mo del of parallel

computation it is not obvious that there are any nontrivial fault mo dels that allow nearlinear

sp eedups esp ecially considering the generally intimidating imp ossibility results for distributed

and parallel computation Thus it was rather surprising when Paris demonstrated in collab orative

work KS that it is p ossible to combine eciency and faulttolerance for many basic algorithms

expressed as concurrentread concurrentwrite crcw prams in a fault mo del KS allowing

any pattern of dynamic failstop pro cessor errors as long as one pro cessor remains alive The

approach and techniques pioneered byParis in his work were shown to b e readily extendible to

all crcw prams In eect any pram algorithm can b e made robust by eciently simulating a

faultfree machine on a faultprone one Pap ers by other researchers followed pursuing similar

problems in related sharedmemory and messagepassing mo dels It was also demonstrated by

Paris in collab orativework that although optimal simulations are p ossible in some mo dels such

oblivious simulations are not necessarily as ecient as handcrafted robust algorithms eg for

the allimp ortantpointer doubling and parallel prex algorithms KS

Paris and colleagues extended the fault mo del to include processor restarts KS arbitrary

initial memory initialization KS and restricted memoryaccess patterns through controlled

memory access KMS

Algorithms and lower b ounds Akey primitive in the ab ovework is the WriteAll op era

tion KS dened as follows using P processors write s into al l locations of an array of size

N where P  N When P N this op eration captures the computational progress that can

b e naturally accomplished in one time unit byapram Iterated WriteAll forms the basis for

the algorithm simulation techniques Therefore improved WriteAll solutions lead to improved

simulations of al l parallel algorithms Under dynamic failures ecient deterministic solutions to

WriteAll ie increasing the faultfree O N work by small p olylogN factors are nonobvious

The rst such solution prop osed byParis in jointwork KS was an algorithm having worst

case work b ound O N P log N log log N

Memoryaccess concurrency is a ma jor source of available redundancy in parallel algorithms

and deterministic robust ie ecient and faulttolerant computation is imp ossible when concur

rent writes are excluded KMS KS Paris b elieved that it should nevertheless b e p ossible to

limit the signicant memoryaccess concurrency that was assumed by existing robust algorithms

Again surprisingly in KMS he showed with his colleagues that concurrent writes are nec

essary only when faults actually o ccur and not in the anticipation of p ossible faults WriteAll

algorithms can b e constructed so that they can b e executed on a faultfree exclusivewrite ma

chine while on a faultprone concurrentwrite machine the numb er of concurrent writes is exactly

the numb er of pro cessor failures encountered during the execution

The WriteAll algorithms for the failstop mo del have optimal ranges of pro cessors for which

the work is O N Optimalityisachieved by taking advantage of parallel slackness Are there

optimal algorithms for the full range of pro cessors N P Paris et al showed that such

algorithms do not exist KS even for the mo dels with instant memory snapshot and arbitrarily

powerful instruction set an adversary can b e constructed that will force any WriteAll algorithm

to do N log N log log N work For memory snaphosts this b ound is tightthere is a simple

algorithm with a matching upp er b ound BKRS

While the current WriteAll lowerupp er b ound gap is relatively small for the failstop mo del

with dynamic failures a much larger gap remains for the mo dels with restarts and asynchronyIt

was conjectured that for WriteAll there is a quadratic lower b ound in this case Together with

several colleagues BKRS Paris constructed the rst sub quadratic deterministic algorithm

log



In the same pap er a N log N lower b ound was shown for the mo del with work O N  P

The b ound stands even if memory snapshots are allowed but in this case there is also a matching

upp er b ound

Paris considered the remaining gaps b etween lower and upp er b ounds to b e interesting op en

problems and intended to pursue their resolution Left unnished was a jointlyauthored mono

graph bringing together the latest results in this area

Typ e theory

Paris Kanellakis made fundamental contributions to the algorithmic analysis and complexity

theoretic understanding of several imp ortant topics in programming language design including

rst and higherorder unication typ e inference for MLlike programming languages and ex

pressiveness in the typ ed lamb da calculus Paris interests in these areas were natural extensions

of his earlier work in logic programming and database theory The work on these topics com

bined a technical exp ertise with a careful understated icono clasm he wanted and succeeded in

changing his colleagues p erceptions of the relevant states of the art

First order unication Unication is a ubiquitous building blo ck in implementations of sophis

ticated programming languages It is for example the workhorse of logic programming engines

and an essential comp onent of compiletime typ e analysis The dual emergence in the s of

logic programming and parallel computation in b oth research and development suggested to

many computer scientists that parallel unication could greatly enhance the p erformance of logic

programming systems In this context Paris collab orative result DKM that rstorder uni

cation is complete for PTIMEin other words as hard as any p olynomialtime problemwas

an interesting technical result with an imp ortant editorial message

The theorem implied that unication was a formidable if not essential b ottleneck in logic

programming any research program that succeeded in parallelizing unicationsaytorun

in subp olynomial timewould have also succeeded in equivalently parallelizing every known

p olynomial time algorithm Because of this seemingly insurmountable or as most researchers

b elieve that PTIME  NC imp ossible hurdle serious attempts to parallelize unication were

largely put aside

The key idea in this pro of of the linear nature of unication due to Paris is that very

simple unication problems can b e constructed whose solution is isomorphic to the computation

of Bo olean logic gates Bo olean values are simulated by pairs of terms that are forced to unify

i the related value is true Since PTIME can b e captured by certain easilyconstructed

p olynomialsized circuits this technology p ermitted any decision problem solvable in p olynomial

time to b e eciently transformed into a unication problem These ideas were eectively reused

to analyze the complexityoftyp e inference

Complexityoftyp e inference Typ e checking is an imp ortant safety feature of programming

languages ensuring that no runtime typ e errors cause programs to go wrong via typ e errors

eg adding p ointers and strings Typ e inference incorp orates typ e checking with automatic

compiletime mechanisms that deduce the typ es of all runtime data Unication is essential to

manytyp e inference algorithms since rstorder terms can characterize data typ es terms are

built via functions like pair list or function over constants suchasinteger b o olean

or type variables having values constrained by term equations

Many functional programming languages eg ML Haskell Miranda based on typ ed lambda

calculus supp ort typ e inference in the presence of socalled parametric polymorphism In simpler

terms these combined features enable programmers to co de implementations of abstract data



The pap er in which this result app eared was edited by the founding editor of the Journal of Logic Programming

J Alan Robinson and was published as the very rst article in that journal

typ es trees stacks queues etc once and reuse the co de on data of dierenttyp es without the

obligation of adding typ e annotation at each use By comparison other languages with compile

time typ e checkingthe canonical example b eing Pascalrequire a pro cedure to b e rep eatedly

co ded for eachdatatypeatwhich it is used the typ e checker requires redundant source co de

eachcopy with dierenttyp e annotation even though identical target co de is generated for each

copy

Although claims had b een made in the researchcommunity that the ML typ e inference

mechanism was ecient Paris b elieved that such claims were unfounded In a striking joint pap er

KM the simpler problem of recognizing typ ecorrect ML programs was shown to b e PSPACE

hard ie as hard as any problem that can b e solved in p olynomial space and furthermore

contained in EXPTIME This result was b oth counterintuitive and surprising The fundamental

technology was extended via additional insights in another jointwork KMM showing the

problem to b e complete for EXPTIME

The pro of technology used in these theorems was a direct descendantofParis earlier work

on unication The additional typ e exibilityintro duced by ML p olymorphism allows the sim

ulation via unication of more p owerful complexityclassesInParis joint pap er KM ML

p olymorphism was used as an iterativemechanism to simulate quantier elimination for Quan

tied Bo olean Formulas resulting in the PSPACEhardness b ound and in KMM the same

to ols were enhanced to simulate arbitrary exp onentialtime computation Later sophisticated

extensions of his idea yielded signicantlower b ounds for other typ ed lamb da calculi

Expressibility Paris was also interested in characterizing complexity classes AC PTIME

PSPACE EXPTIME EXPSPACE by naturally dened classes of typ ed lamb da terms mir

roring earlier work that had b een done in the database community on logic and expressibility

ImmVar Lamb da calculus is the underlying theory of all functional programming lan

guages though its ro ots are found in the mo dern developmentofmathematicallogicParis work

in this area was designed to provide foundations for functional database query languages and

also to rehabilitate the simply typ ed lamb da calculus from a certain computational disrepute

Interest in higherorder typ ed lamb da calculi had b een motivated in part by negative results

that the only expressible functions on the canonical typ e for integers were the extendedpolynomi

als made from addition multiplication and conditional equality with zeronoticeably absentis

exp onentiation subtraction and integer equality These results suggested that the calculus was

no go o d for useful computation

Paris wantedtoshow that this was not the case all feasible computation was comfortably

found within the simply typ ed lamb da calculus The syntactic and esp ecially semantic con

tortions of higherorder calculi of certain mathematical interest could then b e shown to b e

computationally unnecessary The means to this demonstration was a shift in the computa

tion paradigm instead of considering numerical computations Paris suggested co ding database

queries His suggestion was inspired byalamb da calculus enco ding Mai of the decision prob

lem for higherorder logic whichParis prop osed to extend to an enco ding of the complex object

algebra AB a p owerful database query language We briey discuss some relevant details

Quantied Bo olean Formulas allows quantication only over Bo oleans but can b e generalized

by allowing quantication over iterated p owersets of Bo oleans and replacing prop ositional vari

ables by prime formulas x  y where x and y are typ ed to range over the appropriate p owerset

This decision problem for higherorder logic has nonelementary complexity not solvable in any



Given a closed prop ositional formula F where eachvariable X is orb ound is F true under the naive

interpretation

xed stack of exp onentials and can b e used to show that deciding equivalence of twotyp ed

lamb da terms is nonelementary Mey Sta In the related complex ob ject algebra quanti

cation ranges over atomic constants sets and tuples expressing exactly the generic elementary

database queries that are computable in some xed stackofexponentials By implementing the

complex ob jects algebra in the simply typ ed lamb da calculus the data complexity of logical

queries studied in ImmVar could b e replaced bya procedural variant In this pro cedural

implementation the computational p ower of a query is measured by its integer rank describing

the degree of its higherorder functionalityInjointwork Paris b egan implementation of this

research program HKM HK where PTIME was given a precise characterization via query

terms of xed rank

In further sophisticated extensions of this functional framework for descriptive computational

complexityParis succeeded again in collab orativework in providing syntactic characterizations

for many standard complexity classes HK These results rely on complex query evaluation

strategies that use ecient data structures and avoid the redundancies incurred by more usual

reduction strategies in the lamb da calculus At the time of his death Paris was considering

the use of this technical machinery in providing an alternative and p erhaps more comp elling

treatment of the issues addressed by the area of optimal r eduction in the lamb da calculus

Serge Abiteboul

Stanford University and

Institut National de Recherche en Informatique et Automatique INRIA

Gabriel M Kuper

European ComputerIndustry Research Centre ECRC

Harry G Mairson

Brandeis University

Alexander A Shvartsman

Massachusetts Institute of Technology

Moshe Y Vardi

Rice University

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ACM Symp osium on Principles of Database Systems pp

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pp A preliminary version of this pap er Tools for Datalog Boundednessap

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pp

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Kaufmann pp

ase Theory In Handb o ok of The Kan P C Kanellakis Elements of Relational Datab

oretical Computer Science ed AR Meyer M Nivat MS Paterson D Perrin

and J van Leeuwen vol B Chapter North Holland pp

ObjectOrientedDatabases

AK S Abiteb oul and PCKanellakis Object Identity as a Query Language Primitive J

of the ACM to app ear Full version available as Brown Univ Tech Rep CS

AK S Abiteb oul and P C Kanellakis The Two Facets of ObjectOrientedDataModels

IEEE Data Engineering Bulletin pp

AKRW S Abiteb oul P C Kanellakis S Ramaswamy and E Waller Method Schemas J

of Computer and System Sciences to app ear

BDK F Bancilhon C Delob el and P C Kanellakis Building an Ob jectOriented

Database System The Story of O Morgan Kaufmann

CH A K Chandra and D Harel Horn Clause Queries and Generalizations J Logic

Programming pp

HKR G G Hillebrand P C Kanellakis and S Ramaswamy Functional Programming

Formalisms for OODB Methods In Advances in Ob jectOriented Databases

ed A Dogac M Tamer Ozsu A Biliris and T Sellis SpringerVerlag Series F

Computer and Systems Sciences vol Ch pp

Constraint Databases

BDLW M Benedikt G Dong L Libkin and L Wong Relational Expressive Power of

Constraint Query Languages Manuscript

GK D Q Goldin and P C Kanellakis Constraint Query Algebras Manuscript

KG P C Kanellakis and D Q Goldin Constraint Programming and Database Query

Languages Invited pap er Symp osium on Theoretical Asp ects of Computer

Software Springer LNCS pp Sendai Japan April Note Full

version invited to the rst issue of the new journal Constraints

KKR P C Kanellakis G M Kup er and PZRevesz Constraint Query Languages J

Computer and System Sciences sp ecial issue ed Y Sagiv pp

An extended abstract app eared in ACM Symp osium on the Principles

of Database Systems pp

KRVV P C Kanellakis S RamaswamyDEVengro and J S Vitter Indexing for

Data Models with Constraints and Classes J Computer and System Sciences to

app ear sp ecial issue ed C Beeri An extended abstract app eared in ACM

Symp osium on the Principles of Database Systems pp

RK S Ramaswamy and P C Kanellakis OODB Indexing by ClassDivision in

ACM Symp osium on the Management of Data pp

FaultTolerant Paral lel Computation

BKRS J Buss P C Kanellakis P Ragde and A A Shvartsman Paral lel Algorithms with

Processor Failures and Delays J Algorithms to app ear

KMS P C Kanellakis D Michailidis and A A Shvartsman Concurrency Fault

Tolerance in Paral lel Computation Invited pap er International Conference

on Concurrency Theory Springer LNCS vol pp

KMS P C Kanellakis D Michailidis and A A Shvartsman Control ling Memory Access

Concurrency in Ecient FaultTolerant Paral lel Algorithms Nordic Journal of

Computing pp A preliminary version app eared in Inter

national Workshop on Distributed Algorithms pp

KS P C Kanellakis and A A Shvartsman Ecient Paral lel Algorithms Can Be Made

Robust Distributed Computing pp A preliminary v ersion

app eared in ACM Symp osium on Principles of Distributed Computing

pp

KS P C Kanellakis and A A Shvartsman Ecient Paral lel Algorithms On Restartable

FailStop Processors ACM Symp osium on Principles of Distributed

Computing pp

C Kanellakis and A A Shvartsman FaultTolerance and Eciency in Massively KS P

Paral lel Algorithms In Foundations of Dep endable Computing Paradigms

for Dep endable Applications ed G M Ko ob and C G Lau Kluwer

pp

Type Theory

AB S Abiteb oul and C Beeri On the Power of Languages for the Manipulation of

Complex Objects INRIA Research Rep ort

DKM C Dwork P Kanellakis and J C Mitchell On the Sequential Nature of Unication

Journal of Logic Programming

HK G G Hillebrand and P C Kanellakis Functional Database Query Languages as

TypedLambda Calculi of FixedOrder ACM Symp osium on Principles of

Database Systems pp

HK G G Hillebrand and P C Kanellakis On the Expressive Power of SimplyTyped

and LetPolymorphic Lambda Calculi Manuscript

HKM G G Hillebrand P C Kanellakis and H G Mairson Database Query Languages

Embedded in the TypedLambda Calculus Information and Computationto

app ear A preliminary version app eared in the IEEE Symp osium on Logic

in Computer Science pp

HKM G G Hillebrand P C Kanellakis and H G Mairson AnAnalysis of CoreML

Expressive Power and Type Inference International Collo quium on Au

tomata Languages and Programming Springer LNCS pp

Imm N Immerman Relational Queries Computable in Polynomial Time Information

pp and Computation

KMM P C Kanellakis H G Mairson and J C Mitchell Unication and ML TypeRe

construction In Computational Logic Essays in Honor of Alan Robinson

ed JL Lassez and G D Plotkin MIT Press pp

KM P C Kanellakis and J C Mitchell Polymorphic Unication and ML Typing

ACM Symp osium on the Principles of Programming Languages pp

Mai H G Mairson A Simple Proof of a Theorem of Statman Theoretical Computer

Science Septemb er pp

Mey A R Meyer The Inherent Computational Complexity of Theories of Ordered Sets

Pro ceedings of the International Congress of Mathematicians pp

Sta R Statman The Typed Calculus is not Elementary Recursive Theoretical Com

puter Science pp

Var M Y Vardi The Complexity of Relational Query Languages ACM Symp o

sium on Theory of Computing pp