In Memoriam Paris 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 computer science 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 database 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 Greece in to Eleftherios and Argyroula Kanellakis In he received the Diploma in Electrical Engineering 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 Databases sup ervised by Prof C H Papadimitriou In Paris joined the Computer Science Department of Brown University 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 distributed computing 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