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34
Codequest: Scalable source code queries with datalog
 In ECOOP Proceedings
, 2006
"... Abstract. Source code querying tools allow programmers to explore relations between different parts of the code base. This paper describes such a tool, named CodeQuest. It combines two previous proposals, namely the use of logic programming and database systems. As the query language we use safe Dat ..."
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Cited by 42 (0 self)
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Abstract. Source code querying tools allow programmers to explore relations between different parts of the code base. This paper describes such a tool, named CodeQuest. It combines two previous proposals, namely the use of logic programming and database systems. As the query language we use safe Datalog, which was originally introduced in the theory of databases. That provides just the right level of expressiveness; in particular recursion is indispensable for source code queries. Safe Datalog is like Prolog, but all queries are guaranteed to terminate, and there is no need for extralogical annotations. Our implementation of Datalog maps queries to a relational database system. We are thus able to capitalise on the query optimiser provided by such a system. For recursive queries we implement our own optimisations in the translation from Datalog to SQL. Experiments confirm that this strategy yields an efficient, scalable code querying system. 1
A FixedPoint Approach to Stable Matchings and Some Applications
, 2001
"... We describe a fixedpoint based approach to the theory of bipartite stable matchings. By this, we provide a common framework that links together seemingly distant results, like the stable marriage theorem of Gale and Shapley [11], the MenelsohnDulmage theorem [21], the KunduLawler theorem [19], Ta ..."
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Cited by 30 (5 self)
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We describe a fixedpoint based approach to the theory of bipartite stable matchings. By this, we provide a common framework that links together seemingly distant results, like the stable marriage theorem of Gale and Shapley [11], the MenelsohnDulmage theorem [21], the KunduLawler theorem [19], Tarski's fixed point theorem [32], the CantorBernstein theorem, Pym's linking theorem [22, 23] or the monochromatic path theorem of Sands et al. [29]. In this framework, we formulate a matroidgeneralization of the stable marriage theorem and study the lattice structure of generalized stable matchings. Based on the theory of lattice polyhedra and blocking polyhedra, we extend results of Vande Vate [33] and Rothblum [28] on the bipartite stable matching polytope.
Model Generation and State Generation for Disjunctive Logic Programs
, 1995
"... This paper investigates two fixpoint approaches for minimal model reasoning with disjunctive logic programs P. The first one, called model generation [4], is based on an operator T INT P defined on sets of Herbrand interpretations, whose least fixpoint is logically equivalent to the set of minima ..."
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Cited by 25 (10 self)
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This paper investigates two fixpoint approaches for minimal model reasoning with disjunctive logic programs P. The first one, called model generation [4], is based on an operator T INT P defined on sets of Herbrand interpretations, whose least fixpoint is logically equivalent to the set of minimal Herbrand models of the program. The second approach, called state generation [12], uses a fixpoint operator T s P based on hyperresolution. It operates on disjunctive Herbrand states and its least fixpoint is the set of logical consequences of P, the socalled minimal model state of the program. We establish a useful relationship between hyperresolution by T s P and model generation by T INT P . Then we investigate the problem of continuity of the two operators T s P and T INT P . It is known that the operator T s P is continuous [12], and so it reaches its least fixpoint in at most ! steps. On the other hand, the question of whether T INT P is continuous has been open. ...
Checking safety by inductive generalization of counterexamples to induction
 Proc. FMCAD’07
"... Abstract—Scaling verification to large circuits requires some form of abstraction relative to the asserted property. We describe a safety analysis of finitestate systems that generalizes from counterexamples to the inductiveness of the safety specification to inductive invariants. It thus abstracts ..."
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Cited by 20 (6 self)
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Abstract—Scaling verification to large circuits requires some form of abstraction relative to the asserted property. We describe a safety analysis of finitestate systems that generalizes from counterexamples to the inductiveness of the safety specification to inductive invariants. It thus abstracts the system’s state space relative to the property. The analysis either strengthens a safety specification to be inductive or discovers a counterexample to its correctness. The analysis is easily made parallel. We provide experimental data showing how the analysis time decreases with the number of processes on several hard problems. I.
Modal Logic: A Semantic Perspective
 ETHICS
, 1988
"... This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimul ..."
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Cited by 13 (1 self)
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This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all ‘modal’. We conclude by discussing an example which brings many of the ideas we discuss into play: games.
Parsing algorithms based on tree automata
 IN PROC. IWPT
, 2009
"... We investigate several algorithms related to the parsing problem for weighted automata, under the assumption that the input is a string rather than a tree. This assumption is motivated by several natural language processing applications. We provide algorithms for the computation of parseforests, be ..."
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Cited by 8 (5 self)
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We investigate several algorithms related to the parsing problem for weighted automata, under the assumption that the input is a string rather than a tree. This assumption is motivated by several natural language processing applications. We provide algorithms for the computation of parseforests, best tree probability, inside probability (called partition function), and prefix probability. Our algorithms are obtained by extending to weighted tree automata the BarHillel technique, as defined for contextfree grammars.
The HOL Light manual (1.1)
, 2000
"... ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concr ..."
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Cited by 6 (0 self)
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ion is in a precise sense a converse operation to application. Given 49 50 CHAPTER 5. PRIMITIVE BASIS OF HOL LIGHT a variable x and a term t, which may or may not contain x, one can construct the socalled lambdaabstraction x: t, which means `the function of x that yields t'. (In HOL's ASCII concrete syntax the backslash is used, e.g. \x. t.) For example, x: x + 1 is the function that adds one to its argument. Abstractions are not often seen in informal mathematics, but they have at least two merits. First, they allow one to write anonymous functionvalued expressions without naming them (occasionally one sees x 7! t[x] used for this purpose), and since our logic is avowedly higher order, it's desirable to place functions on an equal footing with rstorder objects in this way. Secondly, they make variable dependencies and binding explicit; by contrast in informal mathematics one often writes f(x) in situations where one really means x: f(x). We should give some idea of how ordina...
The Mathematical Import Of Zermelo's WellOrdering Theorem
 Bull. Symbolic Logic
, 1997
"... this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs ..."
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Cited by 5 (1 self)
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this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his wellknown paradox, an early expression of our motif. The motif becomes fully manifest through the study of functions f :
Solving for Set Variables in HigherOrder Theorem Proving
 Proceedings of the 18th International Conference on Automated Deduction
, 2002
"... In higherorder logic, we must consider literals with exible (set variable) heads. Set variables may be instantiated with logical formulas of arbitrary complexity. An alternative to guessing the logical structures of instantiations for set variables is to solve for sets satisfying constraints. U ..."
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Cited by 5 (1 self)
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In higherorder logic, we must consider literals with exible (set variable) heads. Set variables may be instantiated with logical formulas of arbitrary complexity. An alternative to guessing the logical structures of instantiations for set variables is to solve for sets satisfying constraints. Using the KnasterTarski Fixed Point Theorem [ 15 ] , constraints whose solutions require recursive de nitions can be solved as xed points of monotone set functions. In this paper, we consider an approach to higherorder theorem proving which intertwines conventional theorem proving in the form of mating search with generating and solving set constraints.
Some Results on Stable Matchings and Fixed Points
, 2002
"... In this survey paper, we explain some interconnections between fixed point theorems and the theory of stable matchings. Namely, we relate the bipartite matching problems to the KnasterTarski fixed point theorem and the nonbipartite ones to the Kakutani fixed point theorem. We study the natural latt ..."
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Cited by 5 (1 self)
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In this survey paper, we explain some interconnections between fixed point theorems and the theory of stable matchings. Namely, we relate the bipartite matching problems to the KnasterTarski fixed point theorem and the nonbipartite ones to the Kakutani fixed point theorem. We study the natural lattice structure of stable matchings, and deduce some consequences of it, like linear characterizations of stable matching related polyhedra.