Safety Problems Are NP-complete for Flat Integer Programs with Octagonal Loops
Marius Bozga,Radu Iosif,Filip KoneăźNý +2 more
- 19 Jan 2014
- pp 242-261
TL;DR: This paper proves the NP-completeness of the reachability problem for the class of flat counter machines with difference bounds and octagonal relations, labeling the transitions on the loops, and has a potential impact on other problems in program verification.
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Abstract: This paper proves the NP-completeness of the reachability problem for the class of flat counter machines with difference bounds and, more generally, octagonal relations, labeling the transitions on the loops. The proof is based on the fact that the sequence of powers $\{R^i\}_{i=1}^\infty$ of such relations can be encoded as a periodic sequence of matrices, and that both the prefix and the period of this sequence are $2^{{O}||R||_2}$ in the size of the binary encoding ||R||2 of a relation R. This result allows to characterize the complexity of the reachability problem for one of the most studied class of counter machines [6,10], and has a potential impact on other problems in program verification.
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Citations
Taming past LTL and flat counter systems
TL;DR: In this article, it was shown that the reachability problem for flat counters is NP-complete even if LTL admits past-time operators and arithmetical constraints on counters.
18
PTIME Computation of Transitive Closures of Octagonal Relations
Filip Konečný
- 02 Apr 2016
TL;DR: This paper studies difference bounds and octagonal relations and proves that their transitive closure is a PTIME-computable formula in the existential fragment of Presburger arithmetic, marking a significant complexity improvement.
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PTIME Computation of Transitive Closures of Octagonal Relations
TL;DR: In this article, the transitive closure of integer relations is computed in the existential fragment of Presburger arithmetic using a PTIME-computable formula, which marks a significant complexity improvement over the known algorithms.
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Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic
Stéphane Demri,Amit Kumar Dhar,Arnaud Sangnier +2 more
- 22 Sep 2014
TL;DR: It is shown that model-checking flat counter systems over CTL* (with arithmetical constraints on counter values) has the same complexity as the satisfiability problem for Presburger arithmetic.
Equivalence between model-checking flat counter systems and Presburger arithmetic☆
TL;DR: It is shown that model-checking flat counter systems over CTL* (with arithmetical constraints on counter values) has the same complexity as the satisfiability problem for Presburger arithmetic.
8
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