By Giorgio Bacci, Vincent Danos, Ohad Kammar (auth.), Andrea Corradini, Bartek Klin, Corina Cîrstea (eds.)
This publication 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 awarded 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 aid equipment and methods for software program improvement, in addition to adventure with the move of the ensuing applied sciences into business perform. They hide issues within the fields of summary versions and logics, really good versions and calculi, algebraic and coalgebraic semantics, and method specification and verification. The publication additionally contains 6 papers from the CALCO-tools Workshop, colocated with CALCO 2011 and devoted to instruments in response to algebraic and/or coalgebraic principles.
Read Online or Download Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings PDF
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This e-book constitutes the refereed complaints of the 4th foreign convention on Algebra and Coalgebra in computing device 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.
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Extra info for Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings
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. Calcagno, Gardner, and Zarfaty () introduced context logic, a generalisation of separation logic, to provide abstract local reasoning about abstract data structures. , ). , ). 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.
For X = f (X) a formal polynomial system in n variables, G its associated grammar, and V any valuation over a 1-bounded semiring, we have: μfV = V (T (G)) = V (T [n] (G)) = V (G[n] ) = fVh (0). Since the Kleene sequence converges after at most n steps we can compute the least solution even if the semiring is not ω-continuous. Solving Fixed-Point Equations by Derivation Tree Analysis (b) (a) u v x y u z v x y z x y z v x y z (d) (c) u 31 x z v x y z u v x z Fig. 1. 2 Star-distributive Semirings In an ω-continuous semiring we can define the Kleene star operation by a∗ = i≥0 ai , where a0 = 1.
Esparza and M. Luttenberger Theorem 1 ([Kui97]). t. , and μf is equal to the supremum of the Kleene sequence: 0 f (0) f (f (0)) f i (0) ... f i+1 (0) (1) ... Observe that Kleene’s theorem not only guarantees the existence of the least fixed point, but also provides a first approximation method, usually called fixed-point iteration. 3 From Equations to Grammars We illustrate by means of examples how Kleene’s theorem allows us to connect polynomial systems of equations with context-free grammars and the derivation trees associated with them.
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.)