Exact and approximate algorithms for computing a second Hamiltonian cycle

Deligkas, A.; Mertzios, G.B.; Spirakis, P.G.; Zamaraev, V.

Abstract

A classic result by Stockmeyer [Stockmeyer, 1974] gives a non-elementary lower bound to the emptiness problem for star-free generalized regular expressions. This result is intimately connected to the satisfiability problem for interval temporal logic, notably for formulas that make use of the so-called chop operator. Such an operator can indeed be interpreted as the inverse of the concatenation operation on regular languages, and this correspondence enables reductions between non-emptiness of star-free generalized regular expressions and satisfiability of formulas of the interval temporal logic of the chop operator under the homogeneity assumption [Halpern et al., 1983]. In this paper, we study the complexity of the satisfiability problem for a suitable weakening of the chop interval temporal logic, that can be equivalently viewed as a fragment of Halpern and Shoham interval logic featuring the operators B, for "begins", corresponding to the prefix relation on pairs of intervals, and D, for "during", corresponding to the infix relation. The homogeneous models of the considered logic naturally correspond to languages defined by restricted forms of regular expressions, that use union, complementation, and the inverses of the prefix and infix relations.

Citation

Deligkas, A., Mertzios, G., Spirakis, P., & Zamaraev, V. (2020). Exact and approximate algorithms for computing a second Hamiltonian cycle. In J. Esparza, & D. Král (Eds.), 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) (21:1-21:13). https://doi.org/10.4230/lipics.mfcs.2020.27

• Presentation Conference Type: Conference Paper (Published)
• Conference Name: MFCS 2020 (International Symposium on Mathematical Foundations of Computer Science)
• Acceptance Date: Jun 29, 2020
• Online Publication Date: Aug 18, 2020
• Publication Date: 2020
• Deposit Date: Aug 4, 2020
• Publicly Available Date: Sep 11, 2020
• Pages: 21:1-21:13
• Series Title: Leibniz International Proceedings in Informatics (LIPIcs)
• Series ISSN: 1868-8969
• Book Title: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020).
• DOI: https://doi.org/10.4230/lipics.mfcs.2020.27
• Public URL: https://durham-repository.worktribe.com/output/1140398