Hilbert's tenth problem
New Decidability Results Concerning Two-Way Counter Machines
SIAM Journal on Computing
On two-way FA with monotonic counters and quadratic Diophantine equations
Theoretical Computer Science
Safety verification for two-way finite automata with monotonic counters
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Flat Parametric Counter Automata
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Reachability in Succinct and Parametric One-Counter Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Model checking succinct and parametric one-counter automata
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Branching-Time model checking of parametric one-counter automata
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Flat Parametric Counter Automata
Fundamenta Informaticae - Machines, Computations and Universality, Part II
| Hi-index | 5.23 |
For 1 ≤ i ≤ k, let Ri denote pi(y)Fi + Gi, where pi(y) is a polynomial in y with integer coefficients, and Fi, Gi are linear polynomials in x1,..., xn with integer coefficients. Let P(z1,..., zk) be a Presburger relation over the nonnegative integers. We show that the following problem is decidable:Given: R1,..., Rk and a Presburger relation P.Question: Are there nonnegative integer values for y, x1,..., xn such that for these values, (R1,..., Rk) satisfies P? We also give some applications to decision problems concerning counter machines.