Download e-book for kindle: Algebra and Coalgebra in Computer Science: 4th International by Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea

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 laptop technological know-how, 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 way in which those effects can help tools and strategies for software program improvement, in addition to event with the move of the ensuing applied sciences into commercial perform. They hide subject matters within the fields of summary types and logics, really expert versions and calculi, algebraic and coalgebraic semantics, and method specification and verification. The ebook additionally comprises 6 papers from the CALCO-tools Workshop, colocated with CALCO 2011 and devoted to instruments in accordance with algebraic and/or coalgebraic principles.

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A derivation tree t ∈ T (G) is pumpable if it contains a path from its root to one of its leaves in which some variable occurs at least twice. Clearly, every tree of height at least n + 1 is pumpable. It is well-known that a pumpable tree t induces a pumpable factorization w = uvxyz of its yield w such that uv i xy i z ∈ L(G) for every i ≥ 0. In particular, for every i ≥ 0 there is a derivation tree ti that (i) yields uv i xy i z, and (ii) is derived from the same axiom as t. Now we have V (t) + V (t0 ) = V (w) + V (uxz) = V (u)V (v)V (x)V (y)V (z) + V (u)V (x)V (z) V (u) 1 V (x) 1 V (z) + V (u)V (x)V (z) (1-boundedness) = V (uxz) (idempotence) = V (t0 ) Repeating this procedere as long as possible, we eventually arrive from a pumpable tree t to another tree tˆ of height at most n with V (t) + V (tˆ) = V (tˆ).

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 . , semirings in which the law a + a = a holds.

Springer-Verlag Berlin Heidelberg 2011 Abstract Local Reasoning for Program Modules 37 list in the heap, starting from address h. The operation of removing 3 from the set must traverse the list from h. The footprint, therefore, comprises the entire list segment from h up to the node with value 3. With abstract predicates, the abstract footprint corresponds to the concrete footprint and hence, in this case, includes all the elements of the set less than or equal to 3. Consequently, abstract predicates cannot be used to present a local abstract specification for removing 3.

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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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