Read e-book online Algebra and Coalgebra in Computer Science: 4th International 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 complaints of the 4th overseas convention on Algebra and Coalgebra in computing device technology, CALCO 2011, held in Winchester, united kingdom, in August/September 2011. The 21 complete papers provided including four invited talks have been rigorously reviewed and chosen from forty-one submissions. The papers file result of theoretical paintings at the arithmetic of algebras and coalgebras, the best way those effects can aid tools and methods for software program improvement, in addition to event with the move of the ensuing applied sciences into commercial perform. They hide issues within the fields of summary types and logics, really good versions and calculi, algebraic and coalgebraic semantics, and approach specification and verification. The publication 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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Additional resources for Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings

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Let X = f (X) be a formal polynomial system with n equations. For every valuation V over an idempotent and commutative ω-continuous semiring μfV = V (H [n+1] ) . Intuitively, this result states that in order to compute μfV we can safely “forget” the derivation trees of dimension greater than n + 1, which implies that Newton’s method terminates after at most n + 1 iterations. In the rest of the section we study two further classes of idempotent ω-continuous semirings for which a similar result can be proved: idempotence allows to “forget” derivation trees, and compute the least solution exactly after finitely many steps.

A b, which implies a∗ b∗ , we get: (a + b)∗ = a∗ = a∗ + b∗ . Finally, for a last bit of motivation, a recent paper shows that the computation of several types of provenance of datalog queries can be reduced to the problem of (in our terminology) computing the least solution of a formal polynomial system over a commutative semiring S [GKT07]. Specifically, in the case of the why-provenance S is also idempotent and further augmented by the identity a2 = a for all a ∈ Σ. Clearly, such semirings are star-distributive.

Until recently, context logic reasoning has always been justified with respect to an operational semantics defined at the same level of abstraction as the reasoning. Recently, in Dinsdale-Young et al. ([4]), we combined abstract local reasoning with data refinement, to refine abstract module specifications into correct implementations. Filipovi´c, O’Hearn, Torp-Smith, and Yang ([5]); Mijajlovi´c et al. ([9]) previously considered data refinement for local reasoning, studying modules built on the heap model.

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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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