Algebra and Coalgebra in Computer Science: 4th International by Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea PDF

By Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea Corradini, Bartek Klin, Corina Cîrstea (eds.)

ISBN-10: 3642229433

ISBN-13: 9783642229435

This booklet constitutes the refereed lawsuits of the 4th overseas convention on Algebra and Coalgebra in machine technology, CALCO 2011, held in Winchester, united kingdom, in August/September 2011. The 21 complete papers offered including four invited talks have been conscientiously reviewed and chosen from forty-one submissions. The papers document result of theoretical paintings at the arithmetic of algebras and coalgebras, the way in which those effects can help tools and methods for software program improvement, in addition to adventure with the move of the ensuing applied sciences into commercial perform. They hide subject matters within the fields of summary versions and logics, really expert versions and calculi, algebraic and coalgebraic semantics, and process specification and verification. The booklet additionally comprises 6 papers from the CALCO-tools Workshop, colocated with CALCO 2011 and devoted to instruments in response to algebraic and/or coalgebraic principles.

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Then: μfV = V (G). t. G. We sketch a proof of this theorem for the particular case of equation (3). Let us “unfold” the grammar G of (4) by augmenting the nonterminal X with a counter keeping track of the height of a derivation: 24 J. Esparza and M. Luttenberger X 1 X [1] X 2 X [2] X 3 X [3] →c →X 1 → aX 1 X 1 | bX 1 → X 2 | X [1] → aX 2 X 2 | aX [1] X → X 3 | X [2] .. 2 2 | aX X h → aX h−1 X h−1 | aX [h−2] X X [h] → X h | X [h−1] .. X [1] | bX h−1 | aX 2 h−1 X [h−2] | bX h−1 Let G[h] (G h ) be the grammar consisting of those “unfolded” rules whose left-hand side is given by one of the variables of X [h] = {X 0 , X [0] , .

We show that Kleene’s theorem, which not only proves the existence of the least solution, but also provides an algorithm for approximating it, corresponds to approximating G by grammars G[1] , G[1] , . . where G[h] generates the derivation trees of G of height h. We then introduce (Section 4) a faster approximation by grammars H [1] , H [1] , . . where H [h] generates the derivation trees of G of dimension h [EKL08a, EKL10]. We show that this approximation is a generalization of Newton’s method for approximating the zero of a differentiable function, and present a new result about its convergence speed when multiplication is commutative [Lut]2 .

Liveness counterexamples can be found by (coinductively) enumerating all possible states that can be reached via infinite loops and then determining if any of these states constitute valid counterexamples. To demonstrate the power of coinductive logic programming, we show how an interpreter for linear temporal logic can be written very elegantly. In LTL, one checks if a temporal logic formula is true along a path. Temporal operators whose meaning is given in terms of LFP s are realized via tabled logic programming, while those whose meaning is given in terms of GFP s are realized using coinductive logic programming.

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Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings by Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea Corradini, Bartek Klin, Corina Cîrstea (eds.)


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