# 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.

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#### References

SHOWING 1-10 OF 58 REFERENCES

Recursive Abstract State Machines

- Computer Science
- J. Univers. Comput. Sci.
- 1997

This work suggests recursive ASMs, which are essentially a Gurevich abstract state machine and capture recursion properly in the sequential version of the ASM thesis. Expand

Time-bounded random access machines

- Computer Science
- STOC
- 1972

This paper introduces a formal model for random access computers and argues that the model is a good one to use in the theory of computational complexity and shows the existence of a time complexity hierarchy which is finer than any standard abstract computer model. Expand

The Linear Time Hierarchy Theorems for Abstract State Machines and RAMs

- Computer Science, Mathematics
- J. Univers. Comput. Sci.
- 1997

The Linear Time Hierarchy Theorems for random access machines and Gurevich abstract state machines are proved and lower bounds for natural linear time problems are proved. Expand

The Sequential ASM Thesis

- Computer Science, Mathematics
- Bull. EATCS
- 1999

The thesis is that every sequential algorithm, on any level of abstraction, can be viewed as a sequential abstract state machine and its extensions inspired diverse applications of ASMs. Expand

High Level System Design and Analysis Using Abstract State Machines

- Computer Science
- FM-Trends
- 1998

The ASM approach is non-monolithic and integratable at any development level into current design and analysis environments, and enhances traditional operational modelling and analysis techniques. Expand

Choiceless Polynomial Time

- Computer Science, Mathematics
- Ann. Pure Appl. Log.
- 1999

This work attempts to capture the choiceless fragment of PTime, a version of abstract state machines (formerly called evolving algebras) that is to replace arbitrary choice with parallel execution and is more expressive than other PTime logics in the literature. Expand

Kolmogoroff algorithms are stronger than turing machines

- Mathematics
- 1980

A predicate is constructed which is recognizable in real time by a Kolmogoroff algorithm but which is not recognizable in real time by a machine with polynomial accessibility.

Church's Thesis and Principles for Mechanisms

- Computer Science
- 1980

It is argued that Turing's analysis of computation by a human being does not apply directly to mechanical devices, and it is proved that if a device satisfies the principles then its successive states form a computable sequence. Expand

Storage Modification Machines

- Computer Science
- SIAM J. Comput.
- 1980

This paper gives a complete description of the SMM model and its real time equivalence to the so-called successor RAMS and shows the existence of an SMM that performs integer-multiplication in linear time. Expand

On Computable Numbers, with an Application to the Entscheidungsproblem

- Mathematics
- 1937

1. Computing machines. 2. Definitions. Automatic machines. Computing machines. Circle and circle-free numbers. Computable sequences and numbers. 3. Examples of computing machines. 4. Abbreviated… Expand