Reachability in Succinct and Parametric One−Counter Automata
One-counter automata are a fundamental and widely-studied class of infinite-state systems. In this paper we consider one-counter automata with counter updates encoded in binary – which we refer to as the succinct encoding. It is easily seen that the reachability problem for this class of machines is...
| Main Authors: | , , , |
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| Format: | Conference item |
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Springer
2009
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| _version_ | 1797078464274104320 |
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| author | Haase, C Kreutzer, S Ouaknine, J Worrell, J |
| author_facet | Haase, C Kreutzer, S Ouaknine, J Worrell, J |
| author_sort | Haase, C |
| collection | OXFORD |
| description | One-counter automata are a fundamental and widely-studied class of infinite-state systems. In this paper we consider one-counter automata with counter updates encoded in binary – which we refer to as the succinct encoding. It is easily seen that the reachability problem for this class of machines is in PSpace and is NP-hard. One of the main results of this paper is to show that this problem is in fact in NP, and is thus NP-complete. We also consider parametric one-counter automata, in which counter updates be integer-valued parameters. The reachability problem asks whether there are values for the parameters such that a final state can be reached from an initial state. Our second main result shows decidability of the reachability problem for parametric one-counter automata by reduction to existential Presburger arithmetic with divisibility. |
| first_indexed | 2024-03-07T00:32:12Z |
| format | Conference item |
| id | oxford-uuid:80342a86-685d-4a8d-b7c3-9945696287c8 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:32:12Z |
| publishDate | 2009 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:80342a86-685d-4a8d-b7c3-9945696287c82022-03-26T21:21:44ZReachability in Succinct and Parametric One−Counter AutomataConference itemhttp://purl.org/coar/resource_type/c_5794uuid:80342a86-685d-4a8d-b7c3-9945696287c8Department of Computer ScienceSpringer2009Haase, CKreutzer, SOuaknine, JWorrell, JOne-counter automata are a fundamental and widely-studied class of infinite-state systems. In this paper we consider one-counter automata with counter updates encoded in binary – which we refer to as the succinct encoding. It is easily seen that the reachability problem for this class of machines is in PSpace and is NP-hard. One of the main results of this paper is to show that this problem is in fact in NP, and is thus NP-complete. We also consider parametric one-counter automata, in which counter updates be integer-valued parameters. The reachability problem asks whether there are values for the parameters such that a final state can be reached from an initial state. Our second main result shows decidability of the reachability problem for parametric one-counter automata by reduction to existential Presburger arithmetic with divisibility. |
| spellingShingle | Haase, C Kreutzer, S Ouaknine, J Worrell, J Reachability in Succinct and Parametric One−Counter Automata |
| title | Reachability in Succinct and Parametric One−Counter Automata |
| title_full | Reachability in Succinct and Parametric One−Counter Automata |
| title_fullStr | Reachability in Succinct and Parametric One−Counter Automata |
| title_full_unstemmed | Reachability in Succinct and Parametric One−Counter Automata |
| title_short | Reachability in Succinct and Parametric One−Counter Automata |
| title_sort | reachability in succinct and parametric one counter automata |
| work_keys_str_mv | AT haasec reachabilityinsuccinctandparametriconecounterautomata AT kreutzers reachabilityinsuccinctandparametriconecounterautomata AT ouakninej reachabilityinsuccinctandparametriconecounterautomata AT worrellj reachabilityinsuccinctandparametriconecounterautomata |