Reversal-Bounded Multicounter Machines and Their Decision Problems
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
TReX: A Tool for Reachability Analysis of Complex Systems
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
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
Verification of qualitative Z constraints
Theoretical Computer Science
A Logic of Singly Indexed Arrays
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Automatic Verification of Counter Systems With Ranking Function
Electronic Notes in Theoretical Computer Science (ENTCS)
Automatic Verification of Integer Array Programs
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Automata-Based Termination Proofs
CIAA '09 Proceedings of the 14th International Conference on Implementation and Application of Automata
Reachability in Succinct and Parametric One-Counter Automata
CONCUR 2009 Proceedings of the 20th International Conference on Concurrency Theory
Proving termination of tree manipulating programs
ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
Acceleration in convex data-flow analysis
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
What else is decidable about integer arrays?
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Model checking succinct and parametric one-counter automata
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Quantitative robustness analysis of flat timed automata
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
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
Finite automata over structures
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Counter automata for parameterised timing analysis of box-based systems
FOPARA'11 Proceedings of the Second international conference on Foundational and Practical Aspects of Resource Analysis
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 [5]. 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 existence of solutions of a 1-parametric linear Diophantine systems. The latter problem is shown to be decidable, using a number-theoretic argument. Finally, the general reachability problem for parametric flat counter automata with more than one loops is shown to be undecidable, by reduction from Hilbert's Tenth Problem [9]