New Decidability Results Concerning Two-Way Counter Machines
SIAM Journal on Computing
Efficient algorithms for optimum cycle mean and optimum cost to time ratio problems
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
Reversal-Bounded Multicounter Machines and Their Decision Problems
Journal of the ACM (JACM)
Two-Way Counter Machines and Diophantine Equations
Journal of the ACM (JACM)
How to Compose Presburger-Accelerations: Applications to Broadcast Protocols
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Verifying Systems with Infinite but Regular State Spaces
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
Multiple Counters Automata, Safety Analysis and Presburger Arithmetic
CAV '98 Proceedings of the 10th International Conference on Computer Aided Verification
On iterating linear transformations over recognizable sets of integers
Theoretical Computer Science
Computation: finite and infinite machines
Computation: finite and infinite machines
On the solvability of a class of diophantine equations and applications
Theoretical Computer Science
Forward analysis and model checking for trace bounded WSTS
PETRI NETS'11 Proceedings of the 32nd international conference on Applications and theory of Petri Nets
Fast acceleration of ultimately periodic relations
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
When model-checking freeze LTL over counter machines becomes decidable
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Automatic generation of invariants for circular derivations in SUP(LA)
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Deciding conditional termination
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Underapproximation of procedure summaries for integer programs
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Hi-index | 0.00 |
In this paper we study the reachability problem for parametric flat counter automata, in relation with the satisfiability problem of three fragments of integer arithmetic. The equivalence between non-parametric flat counter automata and Presburger arithmetic has been established previously by Comon and Jurski. We simplify their proof by introducing finite state automata defined over alphabets of a special kind of graphs (zigzags). This framework allows one to express also the reachability problem for parametric automata with one control loop as the satisfiability of a 1-parametric linear Diophantine systems. The latter problem is shown to be decidable, using a number-theoretic argument. In general, the reachability problem for parametric flat counter automata with more than one loops is shown to be undecidable, by reduction from Hilbert's Tenth Problem. Finally, we study the relation between flat counter automata, integer arithmetic, and another important class of computational devices, namely the 2-way reversal bounded counter machines.