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Circuits and Expressions over Finite Semirings

Published: 28 August 2018 Publication History

Abstract

The computational complexity of the circuit and expression evaluation problem for finite semirings is considered, where semirings are not assumed to have an additive or a multiplicative identity. The following dichotomy is shown: If a finite semiring is such that (i) the multiplicative semigroup is solvable and (ii) it does not contain a subsemiring with an additive identity 0 and a multiplicative identity 1 ≠ 0, then the circuit evaluation problem is in DET ⊆ NC2, and the expression evaluation problem for the semiring is in TC0. For all other finite semirings, the circuit evaluation problem is P-complete and the expression evaluation problem is NC1-complete. As an application, we determine the complexity of intersection non-emptiness problems for given context-free grammars (regular expressions) with a fixed regular language.

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  • (2018)A Universal Tree Balancing TheoremACM Transactions on Computation Theory10.1145/327815811:1(1-25)Online publication date: 22-Oct-2018

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    cover image ACM Transactions on Computation Theory
    ACM Transactions on Computation Theory  Volume 10, Issue 4
    December 2018
    121 pages
    ISSN:1942-3454
    EISSN:1942-3462
    DOI:10.1145/3271481
    Issue’s Table of Contents
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    Publication History

    Published: 28 August 2018
    Accepted: 01 April 2018
    Revised: 01 February 2018
    Received: 01 November 2017
    Published in TOCT Volume 10, Issue 4

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    Author Tags

    1. Semirings
    2. circuit evaluation problem
    3. expression evaluation

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    • (2018)A Universal Tree Balancing TheoremACM Transactions on Computation Theory10.1145/327815811:1(1-25)Online publication date: 22-Oct-2018

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