Foundations of Software Science and Computational by Prakash Panangaden (auth.), Martin Hofmann (eds.)

By Prakash Panangaden (auth.), Martin Hofmann (eds.)

This e-book constitutes the refereed lawsuits of the 14th foreign convention on Foundations of software program technology and computational buildings, FOSSACS 2011, held in Saarbrücken, Germany, March 26—April three, 2011, as a part of ETAPS 2011, the ecu Joint meetings on conception and perform of software program.

The 30 revised complete papers awarded including one full-paper size invited speak have been conscientiously reviewed and chosen from a hundred submissions. The papers are equipped in topical sections on coalgebra and computability, kind thought, procedure calculi, automata concept, semantics, binding, protection, and software research.

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R / 1. A Λ-simulation from M to N is an I-relation M · N · such that for all i, j ∈ I we have Ri ∈ (ζM , ζN )−1 Λi,j Rj , or equivalently R Λ(ζM , ζN )−1 R. 2. The largest Λ-simulation is called Λ-similarity and written Λ M,N . 3. N is said to Λ-encompass M when for every x ∈ M there is y ∈ N such that, for all i ∈ I, we have x ( ΓM,N,i ) y and y ( ΓN,M,i ) x. In our example, the n-component of TwoSim is 2-nested similarity, and the M,N o-component is the converse of similarity from N to M . The rest of the theory in Sect.

2–3, generalize to the setting of a set I with a constraint theory γ. We replace “conversive” by “γ-conversive”. [0,ℵ0 ] In our nested simulation example, we thus obtain an endofunctor PTwoSim on Preordγnest that maps a nested preordered set A = (A0 , ( A,n ), ( A,o )) to (P [0,ℵ0 ] A0 , Sim( A,n ) ∩ Simc ( A,o ), Simc ( A,o )). We conclude: [0,ℵ ] 0 – (from Thm. 2) Given a final QPTwoSim -coalgebra M , we can use ( M · ,n ) · and ( M ,o ) to characterize 2-nested similarity and similarity, respectively, in countably branching transition systems.

5 we look at the example of 2-nested simulation; this requires a generalization of our theory where relations are replaced by indexed families of relations. 2 Mathematical Preliminaries Definition 1. (Relations) R / 1. For sets X and Y , we write X Y when R is a relation from X to Y , and Rel(X, Y ) for the complete lattice of relations ordered by inclusion. 2. X (=X ) / X is the equality relation on X. 4. Given functions Z (f,g) −1 R X 3. Given relations composite. f /Y S / Z , we write / X and W g X R;S /Z for the R / Y , and a relation X /Y , R / W for the inverse image {(z, w) ∈ Z × W | f (z) R g(w)}.

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