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SIAM J. on Computing

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1972

Volume 1, Issue 4, pp. 281-353


On Languages Accepted in Polynomial Time

Ronald V. Book

SIAM J. Comput. 1, pp. 281-287 (7 pages) | Cited 4 times

Online Publication Date: July 13, 2006

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The family NP (P) of languages accepted by nondeterministic (deterministic) Turing machines operating in polynomial time is distinct from many well-known families of languages defined by tape-bounded or time-bounded Turing machines. In particular, it is shown that NP (P) is not equal to the family of context-sensitive languages, the family of languages accepted by deterministic linear bounded automata, or the family of languages accepted by deterministic Turing machines operating within exponential time.

A Note on the Intersection of Complexity Classes of Functions

Leonard J. Bass

SIAM J. Comput. 1, pp. 288-289 (2 pages)

Online Publication Date: July 13, 2006

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The classes of computable functions defined by a bound on the computation time are shown not to be closed under infinite descending intersection.

Analysis and Synthesis of Sorting Algorithms

C. L. Liu

SIAM J. Comput. 1, pp. 290-304 (15 pages) | Cited 1 time

Online Publication Date: July 13, 2006

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The problem of analyzing and synthesizing sorting algorithms is studied. That is, given a sorting algorithm we want to investigate how it works in a step-by-step manner and consequently to assert that it indeed arranges the objects according to a certain ordering relationship, and conversely, given an ordering relationship according to which a set of objects are to be arranged, we want to determine an algorithm that will yield the desired result.

A Minimum Distance Error-Correcting Parser for Context-Free Languages

Alfred V. Aho and Thomas G. Peterson

SIAM J. Comput. 1, pp. 305-312 (8 pages) | Cited 20 times

Online Publication Date: July 13, 2006

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We assume three types of syntax errors can debase the sentences of a language generated by a context-free grammar: the replacement of a symbol by an incorrect symbol, the insertion of an extraneous symbol, or the deletion of a symbol. We present an algorithm that will parse any input string to completion finding the fewest possible number of errors. On a random access computer the algorithm requires time proportional to the cube of the length of the input.

Compatibility and Complexity of Refinements of the Resolution Principle

Richard B. Kieburtz and David Luckham

SIAM J. Comput. 1, pp. 313-332 (20 pages)

Online Publication Date: July 13, 2006

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This paper studies a number of logically complete search strategies (refinements) for improving the performance of automatic theorem-proving programs based on the resolution principle. These strategies restrict the number of deductions generated by the program at the expense of sometimes missing the shortest proof.
By considering elementary proof-preserving transformations on resolution proof trees, (i) it is shown that the conjunction of set-of-support, resolution-with-merging, and linear form deduction is again a complete refinement; (ii) bounds are obtained on the possible increase in complexity of the proof trees when the linear form and resolution-with-merging refinements are imposed.
Finally, examples are given which demonstrate the savings in time and storage when refinements are used to prove some theorems of moderate difficulty in group theory and ternary boolean algebra.

Real-Time Strict Deterministic Languages

Michael A. Harrison and Ivan M. Havel

SIAM J. Comput. 1, pp. 333-349 (17 pages) | Cited 3 times

Online Publication Date: July 13, 2006

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The family of strict deterministic languages has been studied for its theoretical properties and applications to parsing. In particular, these languages have been shown to be precisely the prefix-free deterministic languages. Deterministic pushdown automata are called (quasi-)real time if they have no (only a bounded number of consecutive) null moves. It is shown that for strict deterministic languages, the quasi-real-time and real-time constraints are equivalent (except for $\{ \Lambda \} $). A grammatical characterization of these languages is also given. For quasi-real-time strict deterministic languages, an easy and elegant decision method is given for testing regularity. For all known methods of accepting deterministic languages, it is shown that the families of real-time languages are a proper subset of the full families. A relation is established among these sets, the simple deterministic languages, and some hierarchies.

Infix to Prefix Translation: The Insufficiency of a Pushdown Stack

Edward M. Reingold

SIAM J. Comput. 1, pp. 350-353 (4 pages)

Online Publication Date: July 13, 2006

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The permutations of the input string achievable by an algorithm which uses a single pushdown stack and $M$ random access storage locations are characterized, and the characterization is used to show that no such algorithm can translate arithmetic expressions from infix to prefix.
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