Safety Verification for Two-Way Finite Automata with Monotonic Counters

Ibarra, Óscar H.; Dang, Zhe; Sun, Zhi-Wei

doi:10.1007/3-540-45005-x_29

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Cited by 2 publications

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“…These equations, given in the Abstract, arose when were investigating certain verification problems concerning counter machines [3] (see also [4]). Actually, the class we consider here is more general in that in [3], the p i (y)'s are linear in y, and the Presburger relation P is of a special form-an "equality" relation.…”

Section: Introductionmentioning

confidence: 98%

On the solvability of a class of diophantine equations and applications

Ibarra

Dang

2006

Theoretical Computer Science

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For 1 i k, let R i denote p i (y)F i + G i , where p i (y) is a polynomial in y with integer coefficients, and F i , G i are linear polynomials in x 1 , . . . , x n with integer coefficients. Let P (z 1 , . . . , z k ) be a Presburger relation over the nonnegative integers. We show that the following problem is decidable:Given: R 1 , . . . , R k and a Presburger relation P.Question: Are there nonnegative integer values for y, x 1 , . . . , x n such that for these values, (R 1 , . . . , R k ) satisfies P? We also give some applications to decision problems concerning counter machines.

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Section: Introductionmentioning

confidence: 98%