ON EQUATIONS OVER SETS OF NUMBERS AND THEIR LIMITATIONS-Reference-Cited by-同舟云学术

ON EQUATIONS OVER SETS OF NUMBERS AND THEIR LIMITATIONS

Published:2011-02 Issue:02 Volume:22 Page:377-393
ISSN:0129-0541
Container-title:International Journal of Foundations of Computer Science
language:en
Short-container-title:Int. J. Found. Comput. Sci.

Author:

LEHTINEN TOMMI¹²,OKHOTIN ALEXANDER³

Affiliation:

1. Department of Mathematics, University of Turku, Turku FI–20014, Finland

2. Turku Centre for Computer Science, Finland

3. Academy of Finland, and Department of Mathematics, University of Turku, Turku FI–20014, Finland

Abstract

Systems of equations of the form X = Y + Z and X = C, in which the unknowns are sets of natural numbers, "+" denotes elementwise sum of sets S + T = {m + n | m ∈ S, n ∈ T}, and C is an ultimately periodic constant, have recently been proved to be computationally universal (Jeż, Okhotin, "Equations over sets of natural numbers with addition only", STACS 2009). This paper establishes some limitations of such systems. A class of sets of numbers that cannot be represented by unique, least or greatest solutions of systems of this form is defined, and a particular set in this class is constructed. The argument is then extended to equations over sets of integers.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S012905411100809X

Reference11 articles.

1. Set Constraints in Some Equational Theories

2. Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth

3. The Power of Commuting with Finite Sets of Words

4. Unrestricted complementation in language equations over a one-letter alphabet

5. The Complexity of Membership Problems for Circuits Over Sets of Natural Numbers

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