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Prognosis of ω-Languages for the Diagnosis of *-Languages: A Topological Perspective

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Abstract

This article offers a novel perspective on the diagnosis of *-languages via a topological characterization of ω-languages. This allows for the different concepts that currently exist in diagnosis of discrete-event systems to be related to one another in a uniform setting and to study their complexity. For this purpose, we introduce the notion of prognosability of an ω-language, which in the classical setting corresponds to testing if a language is diagnosable and prediagnosable. We show that we can build a prognoser for some ω-language if this language is open and saturated, where openness is usually implied in the finitary setting. For both of these problems we present PSPACE algorithms, and establish that prognosability (i.e., whether or not a prognoser exists) for an ω-language is a PSPACE-complete problem. Our new characterization offers a novel point of view in the classical setting of diagnosis.

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References

  • Alpern B, Schneider FB (1987) Recognizing safety and liveness. Distrib Comput 2:117–126

    Article  MATH  Google Scholar 

  • Berstel J (1979) Transductions and context-free languages. Teubner Studienbücher, Stuttgart

    MATH  Google Scholar 

  • Elgot CC, Mezei JE (1965) On relations defined by generalized finite automata. IBM J Res Develop 9:47–68

    MATH  MathSciNet  Google Scholar 

  • Frougny C, Sakarovitch J (1993) Synchronized rational relations of finite and infinite words. Theor Comput Sci 108(1):45–82

    Article  MATH  MathSciNet  Google Scholar 

  • Gire F, Nivat M (1984) Relations rationnelles infinitaires. Calcolo 21(2):91–125

    Article  MATH  MathSciNet  Google Scholar 

  • Grädel E, Thomas W, Wilke T (eds) (2002) Automata, logics, and infinite games: a guide to current research (outcome of a Dagstuhl seminar, February 2001). Lecture Notes in Computer Science, vol 2500. Springer, New York

    Google Scholar 

  • Jeron T, Marchand H, Pinchinat S, Cordier M-O (2006) Supervision patterns in discrete event systems diagnosis. In: 8th workshop on discrete event systems, WODES’06, Ann Arbor

  • Jéron T, Marchand H, Genc S, Lafortune S (2008) Predictability of sequence patterns in discrete event systems. In: IFAC World Congress, Seoul

  • Jiang S, Kumar R (2004) Failure diagnosis of discrete event systems with linear-time temporal logic fault specifications. IEEE Trans Automat Contr 49(6):934–945

    Article  MathSciNet  Google Scholar 

  • Jiang S, Huang Z, Chandra V, Kumar R (2001) A polynomial time algorithm for diagnosability of discrete event systems. IEEE Trans Automat Contr 46(8):1318–1321

    Article  MATH  MathSciNet  Google Scholar 

  • Klarlund N (1991) Progress measures for complementation of omega-automata with applications to temporal logic. In: FOCS. IEEE, pp 358–367

  • Kupferman O, Vardi MY (2001) Model checking of safety properties. Form Methods Syst Des 19(3):291–314

    Article  MATH  MathSciNet  Google Scholar 

  • Landweber LH (1969) Decision problems for omega-automata. Math Syst Theory 3(4):376–384

    Article  MATH  MathSciNet  Google Scholar 

  • McNaughton R (1966) Testing and generating infinite sequences by a finite automaton. Inf Control 9:521–530

    Article  MATH  MathSciNet  Google Scholar 

  • Peled D, Wilke T, Wolper P (1998) An algorithmic approach for checking closure properties of ω-regular languages. Theor Comp Sci 195(2):183–203

    Article  MATH  MathSciNet  Google Scholar 

  • Perrin D, Pin J-E (2004) Infinite words, automata, semigroups, logic and games. Elsevier, Amsterdam

    MATH  Google Scholar 

  • Prieur C (2000) Fonctions rationnelles de mots infinis et continuté. Thèse de Doctorat, Univ. Paris 7

  • Rabin MO, Scott D (1959) Finite automata and their decision problems. IBM J Res Develop 3:114–125

    Article  MathSciNet  Google Scholar 

  • Sampath M, Sengupta R, Lafortune S, Sinaamohideen K, Teneketzis D (1995) Diagnosability of discrete event systems. IEEE Trans Automat Contr 40(9):1555–1575

    Article  MATH  Google Scholar 

  • Sampath M, Sengupta R, Lafortune S, Sinaamohideen K, Teneketzis D (1996) Failure diagnosis using discrete event models. IEEE Trans Control Syst Technol 4(2):105–124

    Article  Google Scholar 

  • Savitch WJ (1970) Relationships between nondeterministic and deterministic tape complexities. J Comput Syst Sci 4:177–192

    MATH  MathSciNet  Google Scholar 

  • Sistla AP (1994) Safety, liveness and fairness in temporal logic. Form Asp Comput 6(5):495–512

    Article  MATH  Google Scholar 

  • Sistla AP, Vardi M, Wolper P (1987) The complementation problem for Buchï automata with applications to temporal logic. Theor Comp Sci 49:217–237

    Article  MATH  MathSciNet  Google Scholar 

  • Staiger L (1997) ω-languages. In: Rozenberg G, Salomaa A (eds) Handbook of formal languages, vol 3: beyond words, chapter 10. Springer, New York, pp 339–388

    Google Scholar 

  • Thomas W (1990) Infinite trees and automaton definable relations over ω-words. In: Proc. STACS 90, Rouen, LNCS 415. Springer, New York

    Google Scholar 

  • Yoo T, Lafortune S (2002) Polynomial-time verification of diagnosability of partially-observed discrete-event systems. IEEE Trans Automat Contr 47(9):1491–1495

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Australian National University, Canberra, Australia

    Andreas Bauer

  2. IRISA, Rennes, France

    Sophie Pinchinat

Authors
  1. Andreas Bauer
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  2. Sophie Pinchinat
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Corresponding author

Correspondence to Sophie Pinchinat.

Additional information

This research was supported by the Marie Curie Scientific Project MASLOG 021669 (FP6-2004-Mobility-6) and Univ. de Rennes 1.

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Bauer, A., Pinchinat, S. Prognosis of ω-Languages for the Diagnosis of *-Languages: A Topological Perspective. Discrete Event Dyn Syst 19, 451–470 (2009). https://doi.org/10.1007/s10626-009-0084-5

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  • DOI: https://doi.org/10.1007/s10626-009-0084-5

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