Evolving algebras 1993: Lipari guide
Specification and validation methods
Sequential abstract-state machines capture sequential algorithms
ACM Transactions on Computational Logic (TOCL)
Abstract state machines capture parallel algorithms
ACM Transactions on Computational Logic (TOCL)
Ordinary interactive small-step algorithms, I
ACM Transactions on Computational Logic (TOCL)
Towards a model execution framework for Eclipse
Proceedings of the 1st Workshop on Behaviour Modelling in Model-Driven Architecture
Persistent queries in the behavioral theory of algorithms
ACM Transactions on Computational Logic (TOCL)
Yuri, logic, and computer science
Fields of logic and computation
Relativity and abstract state machines
SAM'12 Proceedings of the 7th international conference on System Analysis and Modeling: theory and practice
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We consider parallel algorithms working in sequential global time, for example, circuits or parallel random access machines (PRAMs). Parallel abstract state machines (parallel ASMs) are such parallel algorithms, and the parallel ASM thesis asserts that every parallel algorithm is behaviorally equivalent to a parallel ASM. In an earlier article, we axiomatized parallel algorithms, proved the ASM thesis, and proved that every parallel ASM satisfies the axioms. It turned out that we were too timid in formulating the axioms; they did not allow a parallel algorithm to create components on the fly. This restriction did not hinder us from proving that the usual parallel models, like circuits or PRAMs or even alternating Turing machines, satisfy the postulates. But it resulted in an error in our attempt to prove that parallel ASMs always satisfy the postulates. To correct the error, we liberalize our axioms and allow on-the-fly creation of new parallel components. We believe that the improved axioms accurately express what parallel algorithms ought to be. We prove the parallel thesis for the new, corrected notion of parallel algorithms, and we check that parallel ASMs satisfy the new axioms.