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 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 best way those effects can help equipment and methods for software program improvement, in addition to event with the move of the ensuing applied sciences into business perform. They hide themes within the fields of summary types and logics, really expert versions and calculi, algebraic and coalgebraic semantics, and approach 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.

**Read 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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**Additional resources for Algebra and Coalgebra in Computer Science: 4th International Conference, CALCO 2011, Winchester, UK, August 30 – September 2, 2011. Proceedings**

**Example text**

We depict derivation trees in the standard way as ordered finite trees and say that a derivation tree t ∈ T (G) yields a word a1 a2 . . al ∈ Σ ∗ if the i-th leaf from the left of t is labeled by ai . For instance, the following trees t1 , t2 , t3 , t4 yield the words c, bc, acc, abcc, respectively: t1 : X c t2 : X b t3 : X X c a t4 : X X X c c a X X b X c c ... Solving Fixed-Point Equations by Derivation Tree Analysis 23 Note that the grammar G for an univariate equation has only a single nonterminal, and thus the axiom of G is clear.

Xn ) .. Xn = fn (X1 , X2 , . . , Xn ) where X1 , X2 , . . , Xn are variables and f1 , f2 , . . , fn are n-ary functions over some common domain S. ). Loosely speaking, the function fi describes the next state of the i-th component as a function of the current states of all components, and so the solutions of the system describe the equilibrium states. In computer science, a prominent example of fixed-point equations are dataflow equations. g. [NNH99]). Without further assumptions on the functions f1 , .

The tropical semiring N, min, +, ∞, 0 is a prominent example of star-distributive semiring. Actually, any ω-continuous commutative and idempotent semiring in which the natural order is total is star-distributive. g. 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].

### 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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