DOCSLIB.ORG

Author Index

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Author Index Author Index Alagic, S. 104 -Eukasiewics 172 Arbib, M. A. 104 McCuIloch, Warren 126 Boden, Margaret 43 De Morgan, Augustus 11 Boole, George 3 Newman, James R. 178 Cantor, Georg 161 Nilsson, N. J. 126 Descartes, Rene 5 Peano, Giuseppe 34 Euclid 4 Peterson, G. R. 126 Euler, Leonhard 178 Pitts, WaIter 126 Fibonacci 96 Stone, MarshaIl 160 Hill, F. J. 126 Vacroux, A. G. 124 Leonardo of Pisa 96 Venn, John 7 Notation Index .- 1 An 19 xdiv y 2 A~B 19, 160 xmody 2 g·f 20 Z 2 A 20,41 N 3 /\ 47,112 XEA 3 1\ 156 x$A 3 XA 21 PA 3, 111 Q 23 cp 3 .1 23, 158 AcB 3 Pfn[A, B] 23 D 5 ..:... 23 AxB 5 ~ 25 R 5 R 25 2A 6 Ixl 29 IAI 6, 160, 161 n! 35 &l'A 6 (J 38,48,177 AuB 7,43,201 X* 41 AnB 8 In 41 A-B 8 A·B 43,201 Al + ... + An 8 A* 43,44,201 V 47,113 8 U Ai 155 l'5.is.n V 15 48 A 9 qo 48 rnn 12 15* 49,204 f(A) 16 T(M) 50 f:A -+ B 16 v-+w l lw 2 1···IWn 55 a Hf(a) 16 =• 55 n 19 = 55 212 Notation Index .. - 59 O'(n) 115 X* 60 $m 115 e 60 plq 122 {} 63 NAND 122 T 65 NAND-gate 122 ISATOM 66 NOR 123 HEAD 67 L 123 TAIL 67 (P L q) 123 CONS 68 NOR-gate 127 CAR 68 COND 129 CDR 68 A=> B 132 EQ 68 = 133 EQUAL 68 p => q 135 COND 68 (Vx) 141 LxJ 78 (3x) 141 P(n, r) 82 R:A~A 146 nPr 82 ~A 146 nCr 83 n : n' mod m 146 (~) 83 id A 146 T 111 [a] 147 F 111 A modulo: 149 NOT 112 AI: 149 AND 112 :=:; 150 OR 112 Pfo 151 $ 112 (A, v, A) 157 15 112 T 158 -,p 112 ~o 162 NOT-gate 114 ScopeT(v) 169 AND-gate 114 v(w) 169 OR-gate 114 nn 170 max 114 c5 w 171 min 114 0'0 177 Zm 115 0'1 177 n mod m 115 T(M) 200 Subject Index A axiomatization 138 complete 140 absolute value 29 sound 139 accepting states 48 Axiom System for Propositional Logic additive identity 45 138 additive inverse 45 addition of cardinal numbers 165 address of a node in a tree 168 B aleph null 162 Algorithm Analysis 92, 102 Backus-Naur Form (BNF) 59 almost everywhere 154 base 12 alphabet 41 basis step 32, 131 ambiguous tree presentation 94 best possible result 78 analytic geometry 5 biconditional form 130 ancestor 88 bijection 18, 20 antecedent 135 bijective correspondence 19 antisymmetry 150 binary arithmetic progression 13 decision tree 7, 106 Artificial Intelligence (AI) 43 search 60, 104 arity 169, 170 tree 90 arrays 62, 64 tree, complete 92 associative 29 Binomial Theorem 83 operation 44 bipartite graph 186 laws 10 bits 15 atom 65 Boolean 3, 158 average complexity 104 algebra 159 214 Subject Index Boolean (cont.) conjunctive normal form 121, 127 connection matrix 193 connected graph 180 function 118 connectedness relation 179 semiring 47, 190 connection matrices of graphs 193 bottom 23, 158 connection matrix of an FSA 199 box notation for s-expressions 67 construction function 68 branches 88 constructive proof 78 consequent 135 Context-Free Grammars 53, 54 c context-free language 56 canonical surjection 149 contradic tion 137 Cantor's Diagonal Argument 165 contrapositive 132, 136 cardinal number 161 converse 132 cardinali ty 6, 161 corollary 134 carrier 171 cost of a search 103 carry bit 123 counter 64 carry look-ahead adder 126 counting principles 73 Cartesian power 19,42,62 cycle 178 Cartesian product 5, 62, 63 ceiling of x 78 D characteristic function 21,26 codomain 16,22 data type 62 combination 83 daughter 168 comments 63 decimal notation 54 commutative 10, 29 definition commutative mono id 46 domain of 22 compiler 48 formal 47 complemented lattice 159 inductive 64 complete axiomatization 140 recursive 35 complete binary tree 92 Recursive Definition of Addition 39 complete lattice 157 degree of a vertex 185 complexity De Morgan's Laws 11, 113 average 104 denumerable set 163 of switching functions 125 descendants 88 optimal worst-case 109 derivation tree 55 worst-case 103 derives 55 component of a graph 180 diagonal 146 composite 10 dictionary order 152 of maps 20 difference equation 95 of relations 27,153 directed graph 177 computer circuitry 114 directly derives 55 conc function 43 disjoint concatenate 41 partial functions 151 concatenation 43 sets 8 condition sum of partial functions 151 sufficient 132 union 8,42 conditional 135 disjunction 47 conjunct 121, 129 disjunctive normal form 117 conjunction 112,47 disjunctive normal form theorem 120 Subject Index 215 distributive 29 Fibonacci Sequence 95 distributive lattice 159 finite state acceptor (FSA) 48 distributive laws 10 finite state language (FSL) 50, 200 dividend liS floor of x 78 divides II flowcharts 183 domain 16 flow diagram 1, 185 interpretation of an operator forest of trees 90 domain 171 forest, ordered 90 of definition 22 formal definition 47 operator 169, 170 formal language theory 43 tree 168 Four-Color Problem 183 dotted pair 65 full-adder 124 dynamics 199 full binary tree 92 function 16 Boolean 118 E characteristic 21,26 construction 68 E*-connection matrix 193 disjoint partial 151 edges 177 disjoint sum of partial 151 element end 177 maximal 154 factorial 35 minimal 154 Fibonacci 97 empty graph of a function 24 set 3 graph of a partial function 24 sequence 20 identity 146 string 41 length 42 end function 177 monus 23 enumeration 163 partial 17, 22 equivalence class 147 start 177 equivalence (logical) 135 state transition 199 equivalence relation 146, 147 switching 125 Euler path 178 total 22 EuIer's Theorem 181 transition 48 exclusive or 112 functionally complete operations 122 existential quantifier 141 existence proof 78 existence theorem 78 exponents 12 G exponentiation of cardinal numbers 165 grammar of English 53 exponential graph 175 decay 12 bipartite 186 growth 12 component of 180 connected 180 connection matrix 193 F directed 177 of a function 24 factorial function 35 of a partial function 24 false 111 ordered 175 Fibonacci function 97 theory 175 216 Subject Index graph (cont.) interpretation 137 undirected 177 interpretation of an operator domain 71 unordered 175 intersection 8 greatest lower bound (gIb) 156 inverse 20, 45, 47 group 45 additive 45 geometric progression 14 left 28 of a relation 153 right 28 H inverter 114 isolated vertex 180 half-adder 123 isomorphic sets 160 height of a tree 88 isomorphism 20 Hesse diagrams 156 iterate 43 homomorphic image 47 iteration 37 homomorphism 47 iterative solution 64 I J id 20 join 157 identity 44 additive 45 for an operation 44 K function 146 map 20 Konig's lemma 88, 101 matrix 191 Kleene star 43 multiplicative 45 if and only if 133 if ... then . .. else 69, 128 L image 16,22 immediate successor 88 languCfge over X 43 implication 135 latin square 86 impossibility proof 127 orthogonal 86 inclusion relation 150 lattice 157 inclusive or 112 complemented 159 incomparable elements 150 complete 157 induction 57 distributive 159 induction step 32, 131 law inductive definition 64 associative 10 inequality 25 De Morgan's 11, 113 infinite 4 distributive 10 sets 161 leaf 66,169 infinity 160 least upper bound (lub) 155 initial state 48 leaves 87 inorder 93 left inverse 28 input left subtree 90 excitatory 126 lemma 133 inhibitory 126 length 4,41 internal node 87 function 42 Subject Index 217 level in a tree 91 Modus Ponens 139 lexicographic order 152, 160, 173 mono id 44 linear algebra 186 monus 23 linear map 187 multiplication of cardinal numbers 165 Lisp 43, 60, 65 multiplicative identity 45 list 60 mUltiplication modulo m 47 logarithm 12 mutually exclusive events 73 logarithmic search 108 logic Axiom System for Propositional N Logic 138 predicate 140 n-ary predicate 26 propositional 140 n-ary relation 26 loop 177 natural numbers 2, 32 lower bound 156 semiring of 190 L-tree 66 n choose r 83 N-connection matrix 193 NDA 203 necessary and sufficient conditions 133 M necessary conditions 132 negation 111 machine, state-graph of 48 neuron 126 magic square 85 NIL 43,65 magic sum 86 nodes 66,87, 169, 177 map 16, 183 non-constructive proof 78 composite of 20 nondenumerable 166 identity 20 set 164 linear 187 nondeterminism 203 selector 62 nondeterministic finite state acceptor subway 177 (NDA) 203 matrix 187 non-negative integers 3 Boolean connection 193 nonterminals 54 connection matrices of graphs 193 normal form 11 7 connection matrix ofan FSA 199 conjunctive 121, 127 E*-connection 193 disjunctive 117 identity 191 disjunctive normal form theorem 120 N-connection 193 n permute r 82 product of matrices 190 numbers as string of digits 37 sum of 187, 189 symmetric 194 maximal 158 element 154 o maxterm 122 McCulloch-Pitts Neuron 126 il-algebra 171 meet 157 il-trees 172 microcomputers 124 onto 17 minimal 158 one-to-one 18 circuit 124 operator domain 170 element 154 operator label 170 minterm 121 optimal worst-case complexity 109 modulo sum 115 ordered forest 90 218 Subject Index ordered graph 175 proof 138, 139 orthogonallatin square 86 by contradiction 4, 131 outdegree 169 by exhaustion of cases 131 by induction 32, 131 of correctness 104 p techniques 131 propagation of carry bits 125 palindrome 56 proper graph 180 parallelism 126 proper subset 3 parent 88 proposition III parity 84 propositional connectives 140 parity checker 51 propositionallogic 3, 137 parse 53, 203 propositional variable 137 partial function 17, 22 proving theorems 131 disjoint 151 graph of 24 partially ordered set 150 Q partial order 150, 158 partition 153 quantifiers 140 Pascal 47,62 existential 141 path 88 universal 141 of a directed graph 194 quotient 1 Euler 178 length 194 pattern recognition 126 R Peano's Axioms 35 permutations 80, 82 Rabbit breeding 96 Pigeonhole Principle 77, 79 Ramsey's Theorem 80 planar graph 183 range 16,22 poset 150 rational numbers 23 postorder 93, 174 reachable state 199 Polish (prefix) notation 173 Recurrence Relations 95 powerset 6 recursion 32 predicate logic 140 in programming languages
Load more

Recommended publications
  • A Systematic Study of Groebner Basis Methods
    A Systematic Study of Gr¨obner Basis Methods Vom Fachbereich Informatik der Technischen Universit¨at Kaiserslautern genehmigte Habilitationsschrift von Dr. Birgit Reinert Datum der Einreichung: 6. Januar 2003 Datum des wissenschaftlichen Vortrags: 9. Februar 2004 arXiv:0903.2462v2 [math.RA] 29 Mar 2009 Dekan: Prof. Dr. Hans Hagen Habilitationskommission: Vorsitzender: Prof. Dr. Otto Mayer Berichterstatter: Prof. Dr. Klaus E. Madlener Prof. Dr. Teo Mora Prof. Dr. Volker Weispfenning Vorwort Die vorliegende Arbeit ist die Quintessenz meiner Ideen und Erfahrungen, die ich in den letzten Jahren bei meiner Forschung auf dem Gebiet der Gr¨obnerbasen gemacht habe. Meine geistige Heimat war dabei die Arbeitsgruppe von Profes- sor Klaus Madlener an der Technischen Universit¨at Kaiserslautern. Hier habe ich bereits im Studium Bekanntschaft mit der Theorie der Gr¨obnerbasen gemacht und mich w¨ahrend meiner Promotion mit dem Spezialfall dieser Theorie f¨ur Monoid- und Gruppenringe besch¨aftigt. Nach der Promotion konnte ich im Rahmen eines DFG-Forschungsstipendiums zus¨atzlich Problemstellungen und Denkweisen an- derer Arbeitsgruppen kennenlernen - die Arbeitsgruppe von Professor Joachim Neub¨user in Aachen und die Arbeitsgruppe von Professor Theo Mora in Genua. Meine Aufenthalte in diesen Arbeitsgruppen haben meinen Blickwinkel f¨ur weit- ergehende Fragestellungen erweitert. An dieser Stelle m¨ochte ich mich bei allen jenen bedanken, die mich in dieser Zeit begleitet haben und so zum Entstehen und Gelingen dieser Arbeit beigetragen haben. Mein besonderer Dank gilt meinem akademischen Lehrer Professor Klaus Madlener, der meine akademische Ausbildung schon seit dem Grundstudium be- gleitet und meine Denk- und Arbeitsweise wesentlich gepr¨agt hat. Durch ihn habe ich gelernt, mich intensiv mit diesem Thema zu besch¨aftigen und mich dabei nie auf nur einen Blickwinkel zu beschr¨anken.
    [Show full text]
  • Recursion Theory Notes, Fall 2011 0.1 Introduction
    Recursion Theory Notes, Fall 2011 Lecturer: Lou van den Dries 0.1 Introduction Recursion theory (or: theory of computability) is a branch of mathematical logic studying the notion of computability from a rather theoretical point of view. This includes giving a lot of attention to what is not computable, or what is computable relative to any given, not necessarily computable, function. The subject is interesting on philosophical-scientific grounds because of the Church- Turing Thesis and its role in computer science, and because of the intriguing concept of Kolmogorov complexity. This course tries to keep touch with how recursion theory actually impacts mathematics and computer science. This impact is small, but it does exist. Accordingly, the first chapter of the course covers the basics: primitive recur- sion, partial recursive functions and the Church-Turing Thesis, arithmetization and the theorems of Kleene, the halting problem and Rice's theorem, recur- sively enumerable sets, selections and reductions, recursive inseparability, and index systems. (Turing machines are briefly discussed, but the arithmetization is based on a numerical coding of combinators.) The second chapter is devoted to the remarkable negative solution (but with positive aspects) of Hilbert's 10th Problem. This uses only the most basic notions of recursion theory, plus some elementary number theory that is worth knowing in any case; the coding aspects of natural numbers are combined here ingeniously with the arithmetic of the semiring of natural numbers. The last chapter is on Kolmogorov complexity, where concepts of recursion theory are used to define and study notions of randomness and information content.
    [Show full text]
  • Mathematical Society
    Notices of the American Mathematical Society November 1983, Issue 229 Volume 30, Number 7, Pages 713-840 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet­ ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab­ stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions.
    [Show full text]
  • Part IV: Turing Machines and Undecidability
    Part IV: Turing Machines and Undecidability We are about to begin our exploration of the two outer circles of the language hierarchy, as well as the background, the area outside all of the circles. Up until now, we have been placing limitations on what we could do in order that we could discover simple solutions when they exist. Now we are going to tear down all the barriers and explore the full power of formal computation. We will discover a whole range of problems that become solvable once we do that. We will also discover that there are fundamental limitations on what we can compute, regardless of the specific model with which we choose to work. Part IV 264 Turing Machines and Undecidability 17 Turing Machines We need a new kind of automaton that has two properties: • It must be powerful enough to describe all computable things. In this respect, it should be like real computers and unlike FSMs and PDAs. • It must be simple enough that we can reason formally about it. In this respect, it should be like FSMs and PDAs and unlike real computers. 17.1 Definition, Notation and Examples In our discussion of pushdown automata, it became clear that a finite state controller augmented by a single stack was not powerful enough to be able to execute even some very simple programs. What else must be added in order to acquire the necessary power? One answer is a second stack. We will explore that idea in Section 17.5.2. 17.1.1 What Is a Turing Machine? A more straightforward approach is to eliminate the stack and replace it by a more flexible form of infinite storage, a writeable tape.
    [Show full text]
  • Computing the Maximum Using (Min,+) Formulas∗
    Electronic Colloquium on Computational Complexity, Report No. 20 (2018) Computing the maximum using (min,+) formulas∗ Meena Mahajan1, Prajakta Nimbhorkar2, and Anuj Tawari1 1The Institute of Mathematical Sciences, HBNI, Chennai, India , fmeena,[email protected] 2Chennai Mathematical Institute, India , [email protected] January 23, 2018 Abstract We study computation by formulas over (min; +). We consider the computation of maxfx1; : : : ; xng over N as a difference of (min; +) formulas, and show that size n + n log n is sufficient and nec- essary. Our proof also shows that any (min; +) formula computing the minimum of all sums of n − 1 out of n variables must have n log n leaves; this too is tight. Our proofs use a complex- ity measure for (min; +) functions based on minterm-like behaviour and on the entropy of an associated graph. 1 Introduction A (min; +) circuit is a directed acyclic graph (DAG) in which the leaves are labeled by variables or constants. The internal nodes are gates labeled by either min or +. A min gate computes the minimum value among its inputs while a + gate simply adds the values computed by its inputs. If the underlying DAG is a tree, then the circuit is a (min; +) formula. Such formulas can compute any function expressible as the minimum over several linear polynomials with non- negative integer coefficients. That is, they can compute any polynomial over the the tropical − semirings Min = (N; min; +; 1; 0) and Min = (Z; min; +; 1; 0). In this work, we consider the following setting. Suppose we are given n input variables x1; x2; : : : ; xn and we want to find a formula which computes the maximum value taken by these variables, max(x1; x2; : : : ; xn).
    [Show full text]
  • Server Administration Webfocus Reporting Server Release 8205 Datamigrator Server Release 7709
    Server Administration WebFOCUS Reporting Server Release 8205 DataMigrator Server Release 7709 May 20, 2019 Active Technologies, EDA, EDA/SQL, FIDEL, FOCUS, Information Builders, the Information Builders logo, iWay, iWay Software, Parlay, PC/FOCUS, RStat, Table Talk, Web390, WebFOCUS, WebFOCUS Active Technologies, and WebFOCUS Magnify are registered trademarks, and DataMigrator and Hyperstage are trademarks of Information Builders, Inc. Adobe, the Adobe logo, Acrobat, Adobe Reader, Flash, Adobe Flash Builder, Flex, and PostScript are either registered trademarks or trademarks of Adobe Systems Incorporated in the United States and/or other countries. Due to the nature of this material, this document refers to numerous hardware and software products by their trademarks. In most, if not all cases, these designations are claimed as trademarks or registered trademarks by their respective companies. It is not this publisher's intent to use any of these names generically. The reader is therefore cautioned to investigate all claimed trademark rights before using any of these names other than to refer to the product described. Copyright © 2019, by Information Builders, Inc. and iWay Software. All rights reserved. Patent Pending. This manual, or parts thereof, may not be reproduced in any form without the written permission of Information Builders, Inc. Contents Preface ........................................................................ 15 Conventions ........................................................................16 Related Publications
    [Show full text]
  • Proofs, Computability, Undecidability, Complexity, and the Lambda Calculus an Introduction
    Proofs, Computability, Undecidability, Complexity, And the Lambda Calculus An Introduction Jean Gallier and Jocelyn Quaintance Department of Computer and Information Science University of Pennsylvania Philadelphia, PA 19104, USA e-mail: [email protected] c Jean Gallier Please, do not reproduce without permission of the author April 28, 2020 2 Preface The main goal of this book is to present a mix of material dealing with 1. Proof systems. 2. Computability and undecidability. 3. The Lambda Calculus. 4. Some aspects of complexity theory. Historically, the theory of computability and undecidability arose from Hilbert's efforts to completely formalize mathematics and from G¨odel'sfirst incompleteness theorem that showed that such a program was doomed to fail. People realized that to carry out both Hilbert's program and G¨odel'swork it was necessary to define precisely what is the notion of a computable function and the notion of a mechanically checkable proof. The first definition given around 1934 was that of the class of computable function in the sense of Herbrand{ G¨odel{Kleene. The second definition given by Church in 1935-1936 was the notion of a function definable in the λ-calculus. The equivalence of these two definitions was shown by Kleene in 1936. Shortly after in 1936, Turing introduced a third definition, that of a Turing- computable function. Turing proved the equivalence of his definition with the Herbrand{ G¨odel{Kleenedefinition in 1937 (his proofs are rather sketchy compared to Kleene's proofs). All these historical papers can be found in a fascinating book edited by Martin Davis [25].
    [Show full text]
  • CSCE 355 — Foundations of Computation
    CSCE 355 | Foundations of Computation Stephen A. Fenner January 7, 2020 Abstract These notes are based on two lectures per week. Sections beginning test test with a star (*) are optional. The date above is the date of this document's most recent modification. 1 Contents 1 Lecture 1 5 1.0.1 Biconditionals . 6 1.1 Methods of proof . 7 1.1.1 Direct proofs . 7 2 Lecture 2 8 2.0.1 Proof by cases . 8 2.0.2 Proof by induction . 8 2.0.3 Proof by contradiction . 11 3 Lecture 3 12 3.1 Strong induction and the well-ordering principle . 12 3.1.1 * Equivalencep of strong induction and the well-ordering principle . 12 3.2 Proof that 2 is irrational . 13 4 Lecture 4 14 4.1 Describing sets . 14 4.1.1 Listing the elements of a set . 14 4.1.2 Set formers . 15 4.1.3 Don't confuse a set with its members! . 16 4.2 Subsets and the empty set . 16 4.2.1 Proving two sets equal . 17 4.3 Boolean set operations . 17 4.4 Sets of sets, ordered pairs, Cartesian product . 19 4.4.1 * Ordered pairs as sets . 20 4.5 Relations and functions . 21 4.6 The pigeonhole principle . 21 5 Lecture 5 22 5.1 Alphabets, strings, and languages . 22 5.1.1 The concatenation operator . 23 5.1.2 The empty string . 23 5.1.3 Languages . 23 5.1.4 Languages as decision problems . 24 6 Lecture 6 25 6.1 Finite automata .
    [Show full text]
  • A Framework for Automated Concurrency Verification
    A Framework for Automated Concurrency Verification Matthew Bernard Windsor Ph.D University of York Computer Science April 2019 Abstract Reasoning systems based on Concurrent Separation Logic make verifying complex concurrent algorithms readily possible. Such algorithms contain subtle protocols of permission and resource transfer between threads; to cope with these intricacies, modern concurrent separation logics contain many moving parts and integrate many bespoke logical components. Verifying concurrent algorithms by hand consumes much time, effort, and expertise. As a result, computer-assisted verification is a fertile research topic, and fully automated verification is a popular research goal. Unfortunately, the complexity of modern concurrent separation logics makes them hard to automate, and the proliferation and fast turnover of such logics causes a downward pressure against building tools for new logics. As a result, many such logics lack tooling. This dissertation proposes Starling: a scheme for creating concurrent pro- gram logics that are automatable by construction. Starling adapts the existing Concurrent Views Framework for sound concurrent reasoning systems, overlay- ing a framework for reducing concurrent proof outlines to verification conditions in existing theories (such as those accepted by off-the-shelf sequential solvers). This dissertation describes Starling in a bottom-up, modular manner. First, it shows the derivation of a series of general concurrency proof rules from the Views framework. Next, it shows how one such rule leads to the Starling framework itself. From there, it outlines a series of increasingly elaborate frontends: ways of decomposing individual Hoare triples over atomic actions into verification conditions suitable for encoding into backend theories. Each frontend leads to a concurrent program logic.
    [Show full text]
  • Provenance for Aggregate Queries
    Provenance for Aggregate Queries Yael Amsterdamer Daniel Deutch Val Tannen University of Pennsylvania University of Pennsylvania University of Pennsylvania and Tel Aviv University and Ben Gurion University ABSTRACT R We study in this paper provenance information for queries EmpId Dept Sal with aggregation. Provenance information was studied in the 1 d1 20 p1 Dept context of various query languages that do not allow for ag- 2 d1 10 p2 d1 p1 + p2 + p3 gregation, and recent work has suggested to capture prove- 3 d1 15 p3 d2 r1 + r2 nance by annotating the different database tuples with ele- 4 d2 10 r1 ments of a commutative semiring and propagating the anno- 5 d2 15 r2 (b) tations through query evaluation. We show that aggregate queries pose novel challenges rendering this approach inap- (a) plicable. Consequently, we propose a new approach, where we annotate with provenance information not just tuples but Figure 1: Projection on annotated relations also the individual values within tuples, using provenance to ate the polynomials in the security semiring, and propagate describe the values computation. We realize this approach the security annotations through query evaluation (see Sec- in a concrete construction, first for “simple” queries where tion 2.1), assigning security levels to query results. the aggregation operator is the last one applied, and then for Let us briefly illustrate deletion propagation as an appli- arbitrary (positive) relational algebra queries with aggrega- cation of provenance. Consider a simple example of an em- tion; the latter queries are shown to be more challenging in ployee/department/salary relation R shown in Figure 1(a).
    [Show full text]
  • Programming and Symbolic Computation in Maude
    Programming and Symbolic Computation in Maude Francisco Dur´ana, Steven Ekerb, Santiago Escobarc, Narciso Mart´ı-Olietd, Jos´eMeseguere, Rub´enRubiod, Carolyn Talcottb aUniversidad de M´alaga,Spain. bSRI International, CA, USA. cUniversitat Polit`ecnica de Val`encia,Spain. dUniversidad Complutense de Madrid, Spain. eUniversity of Illinois at Urbana-Champaign, IL, USA. Abstract Rewriting logic is both a flexible semantic framework within which widely dif- ferent concurrent systems can be naturally specified and a logical framework in which widely different logics can be specified. Maude programs are exactly rewrite theories. Maude has also a formal environment of verification tools. Symbolic computation is a powerful technique for reasoning about the correct- ness of concurrent systems and for increasing the power of formal tools. We present several new symbolic features of Maude that enhance formal reasoning about Maude programs and the effectiveness of formal tools. They include: (i) very general unification modulo user-definable equational theories, and (ii) symbolic reachability analysis of concurrent systems using narrowing. The pa- per does not focus just on symbolic features: it also describes several other new Maude features, including: (iii) Maude's strategy language for controlling rewriting, and (iv) external objects that allow flexible interaction of Maude object-based concurrent systems with the external world. In particular, meta- interpreters are external objects encapsulating Maude interpreters that can in- teract with many other objects. To make the paper self-contained and give a reasonably complete language overview, we also review the basic Maude features for equational rewriting and rewriting with rules, Maude programming of con- current object systems, and reflection.
    [Show full text]
  • 12.2% 128000 150M Top 1% 154 5200
    We are IntechOpen, the world’s leading publisher of Open Access books Built by scientists, for scientists 5,200 128,000 150M Open access books available International authors and editors Downloads Our authors are among the 154 TOP 1% 12.2% Countries delivered to most cited scientists Contributors from top 500 universities Selection of our books indexed in the Book Citation Index in Web of Science™ Core Collection (BKCI) Interested in publishing with us? Contact [email protected] Numbers displayed above are based on latest data collected. For more information visit www.intechopen.com 20 K-Relations and Beyond Melita Hajdinjak and Andrej Bauer University of Ljubljana Slovenia 1. Introduction Although the theory of relational databases is highly developed and proves its usefulness in practice every day Garcia-Molina et al. (2008), there are situations where the relational model fails to offer adequate formal support. For instance, when querying approximate data Hjaltason & Brooks (2003); Minker (1998) or data within a given range of distance or similarity Hjaltason & Brooks (2003); Patella & Ciaccia (2009). Examples of such similarity-search applications are databases storing images, fingerprints, audio clips or time sequences, text databases with typographical or spelling errors, and text databases where we look for documents that are similar to a given document. A core component of such cooperative systems is a treatment of imprecise data Hajdinjak & Miheliˇc(2006); Minker (1998). At the heart of a cooperative database system is a database where the data domains come equipped with a similarity relation, to denote degrees of similarity rather than simply ‘equal’ and ‘not equal’.
    [Show full text]