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10
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 27 (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.
The power of commuting with finite sets of words
 In Proc. STACS’05, Springer LNCS 3404
, 2005
"... We construct a finite language L such that the largest language commuting with L is not recursively enumerable. This gives a negative answer to the question raised by Conway in 1971 and also strongly disproves Conway’s conjecture on contextfreeness of maximal solutions of systems of semilinear ine ..."
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Cited by 19 (1 self)
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We construct a finite language L such that the largest language commuting with L is not recursively enumerable. This gives a negative answer to the question raised by Conway in 1971 and also strongly disproves Conway’s conjecture on contextfreeness of maximal solutions of systems of semilinear inequalities. 1
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 9 (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.
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 6 (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 Keywords: abstract interpretation, setbased program analysis, types, logic programs, concurrent constraint programs, finite failure, fairness 1
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 5 (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...
Setbased Error Diagnosis of Concurrent Constraint Programs
, 1997
"... We present an automated method for the static prediction of the runtime error `deadlock or failure' in concurrent constraint programs. Operationally, the method is based on a new setbased analysis of reactive logic programs which computes an approximation of the greatestmodel semantics. Semantical ..."
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Cited by 2 (2 self)
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We present an automated method for the static prediction of the runtime error `deadlock or failure' in concurrent constraint programs. Operationally, the method is based on a new setbased analysis of reactive logic programs which computes an approximation of the greatestmodel semantics. Semantically, the method is based on the connection between the inevitability of `deadlock or failure' in concurrent constraint programs, finite failure in logic programming and the greatestmodel semantics over infinite trees.
Tree Schemata and Fair Termination
 Proc. 7 th Int. Symp. SAS ’2000, Santa Barbara, CA, US, LNCS 1824
, 2000
"... We present a new representation for possibly infinite sets of possibly infinite trees. This representation makes extensive use of sharing to achieve efficiency. As much as possible, equivalent substructures are stored in the same place. The new representation is based on a first approximation of ..."
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We present a new representation for possibly infinite sets of possibly infinite trees. This representation makes extensive use of sharing to achieve efficiency. As much as possible, equivalent substructures are stored in the same place. The new representation is based on a first approximation of the sets which has this uniqueness property. This approximation is then refined using powerful representations of possibly infinite relations. The result is a representation which can be used for practical analysis using abstract interpretation techniques. It is more powerful than traditional techniques, and deals well with approximation strategies. We show on a simple example, fair termination, how the expressiveness of the representation can be used to obtain very simple and intuitive analysis.
DECIDING INCLUSION OF SET CONSTANTS OVER INFINITE NONSTRICT DATA STRUCTURES
 THEORETICAL INFORMATICS AND APPLICATIONS
, 1999
"... Various static analyses of functional programming languages that permit infinite data structures make use of set constants like Top, Inf, and Bot, denoting all terms, all lists not eventually ending in Nil, and all nonterminating programs, respectively. We use a set language that permits union, con ..."
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Various static analyses of functional programming languages that permit infinite data structures make use of set constants like Top, Inf, and Bot, denoting all terms, all lists not eventually ending in Nil, and all nonterminating programs, respectively. We use a set language that permits union, constructors and recursive definition of set constants with a greatest fixpoint semantics in the set of all, also infinite, computable trees, where all term constructors are nonstrict. This paper proves decidability, in particular DEXPTIMEcompleteness, of inclusion of coinductively defined sets by using algorithms and results from tree automata and set constraints. The test for set inclusion is required by certain strictness analysis algorithms in lazy functional programming languages and could also be the basis for further setbased analyses.