By Egon Börger (auth.), Yuri Gurevich, Philipp W. Kutter, Martin Odersky, Lothar Thiele (eds.)

This e-book constitutes the completely refereed post-proceedings of the foreign Workshop on summary kingdom Machines, ASM 2000, held in Monte Verita, Switzerland in March 2000.
The 12 revised complete papers offered have been rigorously reviewed and chosen from 30 submissions. additionally incorporated are an introductory assessment, experiences on commercial ASM purposes, in addition to six contributions in response to invited talks. All in all, the quantity safely offers the cutting-edge in examine and functions of summary kingdom machines.

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Extra info for Abstract State Machines - Theory and Applications: International Workshop, ASM 2000 Monte Verità , Switzerland, March 19–24, 2000 Proceedings

Example text

If Mode = 0 then forall x ∈ Atoms do Reached (x) := {x}, Paths(x, x) := {{x}}, Frontier (x) := {x} enddo, Mode := 1 endif, if Mode = 1 then forall x ∈ Atoms do Old Frontier (x) := Frontier (x), Frontier (x) := {y : y ∈ Atoms : y ∈ Reached (x) and {z : z ∈ Frontier (x) : E(z, y)} = ∅} enddo, Mode := 2 endif, if Mode = 2 then forall x ∈ Atoms do forall y ∈ Frontier (x) do Paths(x, y) := {(p, y) : p ∈ {Paths(x, z) : z ∈ Old Frontier (x) : E(z, y)} : true} enddo, Reached (x) := Reached (x) ∪ Frontier (x) enddo, Halt := {Frontier (x) : x ∈ Atoms : true} = ∅, Mode := 1 endif.

A state machines framework with many compositionality properties is also developed in [5] aimed at compiler construction. Paper [3], which gives many references on the study of the refinement, is concentrated on interactive systems and compositionality. There is no time explicitly involved. With respect to compositionality our case is different because of real-time constraints, and we have not yet studied this topic. 2 Asynchronous Distributed Algorithms and Their Timed Semantics Introducing explicit time we pursue two goals: first, to give a unified and intuitive view on semantics and verification proofs and, second, to give possibility to introduce time constraints in specifications of algorithm when refining it or when making precisions of initial formulation.

The result Π(A) of applying this set-new statement Π to a structure A, equals A in the interpretations of every relation name other than Y . In order to define the domain of Π(A) and its interpretation of Y , consider the binary relation S = {(a, b) ∈ A2 | A |= ϕ(a, b)}. 4 Now the domain of Π(A) is that of A, extended with as many new elements as there are different sets in the range of S. Let ι be an arbitrary bijection between the range of S and these new elements. Then the interpretation of Y in Π(A) is defined as {(a, ι(S(a))) | ∃b : S(a, b)}.

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