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22
Setbased Analysis of Reactive Infinitestate Systems
, 1997
"... We present an automated abstract verification method for infinitestate systems specified by logic programs (which are a uniform and intermediate layer to which diverse formalisms such as transition systems, pushdown processes and while programs can be mapped). We establish connections between: logi ..."
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Cited by 26 (8 self)
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We present an automated abstract verification method for infinitestate systems specified by logic programs (which are a uniform and intermediate layer to which diverse formalisms such as transition systems, pushdown processes and while programs can be mapped). We establish connections between: logic program semantics and CTL properties, setbased program analysis and pushdown processes, and also between model checking and constraint solving, viz. theorem proving. We show that setbased analysis can be used to compute supersets of the values of program variables in the states that satisfy a given CTL property.
Codefinite Set Constraints
 Proceedings of the 9th International Conference on Rewriting Techniques and Applications, volume 1379 of LNCS
"... In this paper, we introduce the class of codefinite set constraints. This is a natural subclass of set constraints which, when satisfiable, have a greatest solution. It is practically motivated by the setbased analysis of logic programs with the greatestmodel semantics. We present an algorithm so ..."
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Cited by 18 (8 self)
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In this paper, we introduce the class of codefinite set constraints. This is a natural subclass of set constraints which, when satisfiable, have a greatest solution. It is practically motivated by the setbased analysis of logic programs with the greatestmodel semantics. We present an algorithm solving codefinite set constraints and show that their satisfiability problem is DEXPTIMEcomplete. 1 Introduction Set constraints and setbased analysis form an established research topic. It combines theoretical investigations ranging from expressiveness and decidability to program semantics and domain theory, with direct practical applications to type inference, optimization and verification of imperative, functional, logic and reactive programs (see [1, 14, 20] for overviews). In setbased analysis, the problem of reasoning about runtime properties of programs is transferred to the problem of solving set constraints. The design of a system for a particular program analysis problem (for a...
Automata on DAG Representations of Finite Trees
, 1999
"... We introduce a new class of finite automata. They are usual bottomup tree automata that run on DAG representations of finite trees. We prove that the emptiness problem for this class of automata is NPcomplete. Using these automata we prove the decidability of directional type checking for logic ..."
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Cited by 13 (0 self)
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We introduce a new class of finite automata. They are usual bottomup tree automata that run on DAG representations of finite trees. We prove that the emptiness problem for this class of automata is NPcomplete. Using these automata we prove the decidability of directional type checking for logic programs, and thus we improve earlier results by Aiken and Lakshman. We also show an application of these automata in solving systems of set constraints, which gives a new view on the satisfiability problem for set constraints with negative constraints. Keywords Tree Automata, Directed Acyclic Graphs, Types in Logic Programming, Semantics of Logic Programs, Set Constraints 1 Introduction We introduce a new class of finite automata, which we call automata on tdags. They are usual bottomup tree automata that run on DAG representations of ground terms over given signature. The class of languages recognizable by these automata contains all DAG representations of regular sets of terms...
The Horn Mucalculus
, 1998
"... The Horn calculus is a logic programming language allowing arbitrary nesting of least and greatest fixed points. The Horn programs can naturally expresses safety and liveness properties for reactive systems. We extend the setbased analysis of classical logic programs by mapping arbitrary program ..."
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Cited by 13 (9 self)
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The Horn calculus is a logic programming language allowing arbitrary nesting of least and greatest fixed points. The Horn programs can naturally expresses safety and liveness properties for reactive systems. We extend the setbased analysis of classical logic programs by mapping arbitrary programs into "uniform" programs. Our two main results are that uniform programs express regular sets of trees and that emptiness for uniform programs is EXPTIMEcomplete. Hence we have a nontrivial decidable relaxation for the Horn calculus. In a different reading, the results express a kind of robustness of the notion of regularity: alternating Rabin tree automata preserve the same expressiveness and algorithmic complexity if we extend them with pushdown transition rules (in the same way B uchi extended word automata to canonical systems).
Improving the Representation of Infinite Trees to Deal with Sets of Trees
 In ESOP ’00 [ESOP00
, 2000
"... In order to deal efficiently with infinite regular trees (or other pointed graph structures), we give new algorithms to store such structures. ..."
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Cited by 11 (1 self)
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In order to deal efficiently with infinite regular trees (or other pointed graph structures), we give new algorithms to store such structures.
Entailment of Atomic Set Constraints is PSPACEComplete
 In Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science (LICS
, 1999
"... The complexity of set constraints has been extensively studied over the last years and was often found quite high. At the lower end of expressiveness, there are atomic set constraints which are conjunctions of inclusions t 1 t 2 between firstorder terms without set operators. It is wellknown that ..."
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Cited by 8 (5 self)
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The complexity of set constraints has been extensively studied over the last years and was often found quite high. At the lower end of expressiveness, there are atomic set constraints which are conjunctions of inclusions t 1 t 2 between firstorder terms without set operators. It is wellknown that satisfiability of atomic set constraints can be tested in cubic time. Also, entailment of atomic set constraints has been claimed decidable in polynomial time. We refute this claim. We show that entailment between atomic set constraints can express validity of quantified boolean formulas and is thus PSPACE hard. For infinite signatures, we also present a PSPACEalgorithm for solving atomic set constraints with negation. This proves that entailment of atomic set constraints is PSPACEcomplete for infinite signatures. In case of finite signatures, this problem is even DEXPTIMEhard.
SetBased Failure Analysis for Logic Programs and Concurrent Constraint Programs
 PROGRAMMING LANGUAGES AND SYSTEMS, 8TH EUROPEAN SYMPOSIUM ON PROGRAMMING, ESOP'99, VOLUME 1576 OF LNCS
, 1999
"... This paper presents the first approximation method of the finitefailure set of a logic program by setbased analysis. In a dual view, the method yields a type analysis for programs with ongoing behaviors (perpetual processes). Our technical contributions are (1) the semantical characterization ..."
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Cited by 7 (1 self)
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This paper presents the first approximation method of the finitefailure set of a logic program by setbased analysis. In a dual view, the method yields a type analysis for programs with ongoing behaviors (perpetual processes). Our technical contributions are (1) the semantical characterization of finite failure of logic programs over infinite trees and (2) the design and soundness proof of the first setbased analysis of logic programs with the greatestmodel semantics. Finally, we exhibit the connection between finite failure and the inevitability of the `inconsistentstore ' error in fair executions of concurrent constraint programs where no process suspends forever. This indicates a potential application to error diagnosis for concurrent constraint programs.
Applications of an Extended Set Constraint Solver
 In Proc. of the ERCIM / CompulogNet Workshop on Constraints
, 2000
"... . In this paper we present some applications of a set constraint solver, Cardinal, that extends constraint solving to set variables with attached set functions and with special inferences over them. In particular, diagnosis of digital circuits and set covering problems are addressed with exper ..."
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Cited by 5 (1 self)
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. In this paper we present some applications of a set constraint solver, Cardinal, that extends constraint solving to set variables with attached set functions and with special inferences over them. In particular, diagnosis of digital circuits and set covering problems are addressed with experimental results which are compared to other approaches to attest the expressiveness and efficiency of Cardinal. Future extensions of Cardinal are also discussed for other applications such as timetabling and other scheduling problems. 1. INTRODUCTION Set constraints have deserved in the last years special attention by the Constraint Programming community and have been addressed in recent literature for setbased program analysis [1] and for general setbased combinatorial search problems [2,3], producing many interesting theoretical and practical results [4,5,6] making it a very rich and promising research topic [7,8]. In fact, set constraints are a very natural and concise way to exp...
DECISION PROCEDURES FOR EQUATIONALLY BASED REASONING
, 2008
"... This work develops new automated reasoning techniques for verifying the correctness of equationally specified programs. These techniques are not just theoretical, but have been implemented, and applied to actual program verification projects. Although the work spans several different areas, a major ..."
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Cited by 5 (0 self)
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This work develops new automated reasoning techniques for verifying the correctness of equationally specified programs. These techniques are not just theoretical, but have been implemented, and applied to actual program verification projects. Although the work spans several different areas, a major theme of this work is to develop better techniques at the boundary between decidable and undecidable problems. That is, this work seeks out not just positive decidability results, but ways to extend the underlying techniques to be effective on problems outside of decidable subclasses. For program verification to succeed, we feel that two important directions must be pursued: (1) considering more expressive logics to allow designers to more easily specify systems, and (2) develop decision procedures that can reason efficiently about these more sophsticated logics. This work pursues both directions, and the main topics addressed include: new decidability and undecidability results for equational tree automata (Chapter 3), ordersorted unification (Chapter 4), sufficient completeness for specifications with partiality