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Download Automated Reasoning: 4th International Joint Conference, by Aarti Gupta (auth.), Alessandro Armando, Peter Baumgartner, PDF

By Aarti Gupta (auth.), Alessandro Armando, Peter Baumgartner, Gilles Dowek (eds.)

This ebook constitutes the refereed lawsuits of the 4th overseas Joint convention on automatic Reasoning, IJCAR 2008, held in Sydney, Australia, in August 2008.

The 26 revised complete examine papers and thirteen revised approach descriptions offered including four invited papers and a precis of the CASC-J4 platforms festival have been conscientiously reviewed and chosen from eighty complete paper and 17 method description submissions. The papers deal with the full spectrum of study in automatic reasoning and are prepared in topical sections on particular theories, automatic verification, protocol verification, approach descriptions, modal logics, description logics, equational theories, theorem proving, CASC, the 4th IJCAR ATP procedure festival, logical frameworks, and tree automata.

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Extra info for Automated Reasoning: 4th International Joint Conference, IJCAR 2008 Sydney, Australia, August 12-15, 2008 Proceedings

Example text

Iosif, and S. Perarnau is valid iff the set [[ϕ]] [[ψ]] is empty, where is an operator defined on SGRs, that computes the representation of the difference between the set of concrete models of the ϕ and the one of ψ. Least, the emptiness problem for sets of SGRs is shown to be decidable, by reduction to the satisfiability problem for the Presburger arithmetic. 1 Symbolic Shape Graphs In this section we define a finite representation of (possibly infinite) sets of heaps, called symbolic shape graphs (SSG), which is the essence of our decision method.

Note that we use the “classical” (non-intuitionistic) semantics of Separation Logic [15], in which a points-to relation L1 → L2 is true iff the heap is defined on only one cell whose address is the value of L1 . As a result, lsk (L1 , L2 ) is true iff the heap is defined only on the set of addresses that form the list from L1 up to (but not including) L2 . Another consequence of using this semantics is that ls0 (L1 , L2 ) is true only on the empty heap. One can however recover the intuitionistic semantics of [21] by using the k shorthands L1 → L2 and ls (L1 , L2 ) instead.

This paper presents an extension of a decidable fragment of Separation Logic for singly-linked lists, defined by Berdine, Calcagno and O’Hearn [8]. Our main extension consists in introducing atomic formulae of the form lsk (x, y) describing a list segment of length k, stretching from x to y, where k is a logical variable interpreted over positive natural numbers, that may occur further inside Presburger constraints. We study the decidability of the full first-order logic combining unrestricted quantification of arithmetic and location variables.

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