# Sequential abstract-state machines capture sequential algorithms

@article{Gurevich2000SequentialAM, title={Sequential abstract-state machines capture sequential algorithms}, author={Yuri Gurevich}, journal={ACM Trans. Comput. Log.}, year={2000}, volume={1}, pages={77-111} }

We examine sequential algorithms and formulate a sequential-time postulate, an abstract-state postulate, and a bounded-exploration postulate . Analysis of the postulates leads us to the notion of sequential abstract-state machine and to the theorem in the title. First we treat sequential algorithms that are deterministic and noninteractive. Then we consider sequential algorithms that may be nondeterministic and that may interact with their environments.

## 484 Citations

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- 2015

The semantics of concurrent ASMs are defined by concurrent ASM runs which overcome the problems of Gurevich's distributed ASM Runs and generalize Lamport's sequentially consistent runs to form a postulate characterizing an intuitive understanding of concurrency.

Abstract state machines capture parallel algorithms

- Computer ScienceTOCL
- 2003

It is shown that every parallel, synchronous algorithm can be simulated, step for step, by an abstract state machine with a background that provides for multisets.

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- Computer Science, MathematicsArXiv
- 2018

A computational interpretation of the rule of dependent choice is developed which is phrased purely on the level of algorithms, giving a clearer insight into the computational meaning of proofs in classical analysis.

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- 2006

This report consists of two separate parts, essentially two oversized footnotes to the article "Sequential Abstract State Machines Capture Sequential Algorithms" by Yuri Gurevich. In Chapter I, Yuri…

A Verification Approach for Distributed Abstract State Machines

- Computer Science, MathematicsErshov Memorial Conference
- 2001

This paper shows how a transition level in form of a transition graph may be constructed and can be carried out directly on the transition graph to prove properties related to the state transition level induced by partially ordered runs.

A Behavioural Theory of Recursive Algorithms

- Computer Science
- 2020

An axiomatic deﬁnition of the notion of sequential recursive algorithm is proposed which extends Gurevich’s axioms for sequential algorithms by a Recursion Postulate and allows us to prove that sequential recursive algorithms are captured by recursive Abstract State Machines, an extension of nd-seq ASMs by a CALL rule.

Simulation of Timed Abstract State Machines with Predicate Logic Model-Checking

- Computer ScienceJ. Univers. Comput. Sci.
- 2008

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- MathematicsComput. Artif. Intell.
- 2003

The Abstract-State Machine model is characterized as a special class of transition systems that widely extends the class of "computable" transition systems.

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- Computer ScienceActa Informatica
- 2003

This work critically examines Gurevich's requirements for sequential algorithms, as well as the semantics of ASM-programs and the proof of his main theorem.

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