Model checking (MC) for Halpern and Shoham's interval temporal logic HS has been recently shown to be decidable. An intriguing open question is its exact complexity for full HS: it is at least EXPSPACE-hard, and the only known upper bound, which exploits an abstract representation of Kripke structure paths (descriptor), is non-elementary. In this paper, we provide a uniform framework to MC for full HS and meaningful fragments of it, with a specific type of descriptor for each fragment. Then, we devise a general MC alternating algorithm, parameterized by the descriptor's type, which has a polynomially bounded number of alternations and whose running time is bounded by the length of minimal representatives of descriptors (certificates). We analyze its complexity and give tight bounds on the length of certificates. For two types of descriptor, we obtain exponential upper and lower bounds; for the other ones, we provide non-elementary lower bounds.

Complexity analysis of a unifying algorithm for model checking interval temporal logic / Bozzelli, L.; Montanari, A.; Peron, A.. - In: INFORMATION AND COMPUTATION. - ISSN 0890-5401. - 280:(2021). [10.1016/j.ic.2020.104640]

Complexity analysis of a unifying algorithm for model checking interval temporal logic

Bozzelli L.;Montanari A.;Peron A.
2021

Abstract

Model checking (MC) for Halpern and Shoham's interval temporal logic HS has been recently shown to be decidable. An intriguing open question is its exact complexity for full HS: it is at least EXPSPACE-hard, and the only known upper bound, which exploits an abstract representation of Kripke structure paths (descriptor), is non-elementary. In this paper, we provide a uniform framework to MC for full HS and meaningful fragments of it, with a specific type of descriptor for each fragment. Then, we devise a general MC alternating algorithm, parameterized by the descriptor's type, which has a polynomially bounded number of alternations and whose running time is bounded by the length of minimal representatives of descriptors (certificates). We analyze its complexity and give tight bounds on the length of certificates. For two types of descriptor, we obtain exponential upper and lower bounds; for the other ones, we provide non-elementary lower bounds.
2021
Complexity analysis of a unifying algorithm for model checking interval temporal logic / Bozzelli, L.; Montanari, A.; Peron, A.. - In: INFORMATION AND COMPUTATION. - ISSN 0890-5401. - 280:(2021). [10.1016/j.ic.2020.104640]
File in questo prodotto:
File Dimensione Formato  
Complexity-analysis-of-a-unifying-algorithm-for-model-checking-interval-temporal-logic2020Information-and-Computation.pdf

non disponibili

Descrizione: Articolo principale
Tipologia: Documento in Pre-print
Licenza: Accesso privato/ristretto
Dimensione 835.05 kB
Formato Adobe PDF
835.05 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/828979
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact