Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-12T17:55:10.528Z Has data issue: false hasContentIssue false
  • English
  • Français

k-counting automata

Published online by Cambridge University Press:  10 October 2012

Joël Allred and
Ulrich Ultes-Nitsche
Joël Allred
Affiliation:
Department of Computer Science, University of Fribourg, Boulevard de Pérolles 90, 1700 Fribourg, Switzerland,. joel.allred@unifr.ch, uun@unifr.ch.
Ulrich Ultes-Nitsche
Affiliation:
Department of Computer Science, University of Fribourg, Boulevard de Pérolles 90, 1700 Fribourg, Switzerland,. joel.allred@unifr.ch, uun@unifr.ch.

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper, we define k-counting automata as recognizers forω-languages, i.e. languages of infinite words. Weprove that the class of ω-languages they recognize is a proper extensionof the ω-regular languages. In addition we prove that languagesrecognized by k-counting automata are closed under Boolean operations. Itremains an open problem whether or not emptiness is decidable fork-counting automata. However, we conjecture strongly that it is decidableand give formal reasons why we believe so.

Keywords

ω-automataextensions to regularω-languagesclosure under Boolean operationsemptiness probleminfinite hierarchy ofω-languages

References

Alpern, B. and Schneider, F.B., Defining liveness. Inf. Process. Lett. 21 (1985) 181–185. Google Scholar
M. Bojanczyk, Beyond ω-regular languages, in Proc. STACS, LIPIcs, edited by J.-Y. Marion and T. Schwentick. Schloss Dagstuhl – Leibniz-Zentrum für Informatik 5 (2010) 11–16.
M. Bojanczyk and T. Colcombet, Boundedness in languages of infinite words. Unpublished manuscript. Extended version of M. Bojanczyk and T. Colcombet, Bounds in ω-Regularity, in LICS (2006) 285–296.
Bojańczyk, M., David, C., Muscholl, A., Schwentick, T. and Segoufin, L., Two-variable logic on data words. ACM Trans. Comput. Logic 12 (2011) 27 :1–27 :26. Google Scholar
J.R. Büchi, On a decision method in restricted second order arithmetic, in Proc. of the International Congress on Logic, Methodology and Philosophy of Science 1960, edited by E. Nagel et al. Stanford University Press (1962) 1–11.
Fernau, H. and Stiebe, R., Blind counter automata on ω-words. Fundam. Inform. 83 (2008) 51–64. Google Scholar
Fischer, P.C., Turing machines with restricted memory access. Inf. Control 9 (1966) 364–379. Google Scholar
Hashiguchi, K., Algorithms for determining relative star height and star height. Inf. Comput. 78 (1988) 124–169. Google Scholar
J.E. Hopcroft, R. Motwani and J.D. Ullman, Introduction to Automata Theory, Languages and Computation. Addison Wesley, Pearson Education (2006).
Karp, R.M. and Miller, R.E., Parallel program schemata. J. Comput. Syst. Sci. 3 (1969) 147–195. Google Scholar
R.P. Kurshan, Computer-Aided Verification of Coordinating Processes, 1st edition. Princeton University Press, Princeton, New Jersey (1994).
E.W. Mayr, An algorithm for the general petri net reachability problem, in Proc of the 13th Annual ACM Symposium on Theory of Computing, STOC’81. New York, USA, ACM (1981) 238–246.
McNaughton, R., Testing and generating infinite sequences by a finite automaton. Inf. Control 9 (1966) 521–530. Google Scholar
Minsky, M.L., Recursive unsolvability of post’s problem of “tag” and other topics in theory of turing machines. Ann. Math. 74 (1961) 437–455. Google Scholar
D.E. Muller, Infinite sequences and infinite machines, in AIEE Proc. of the 4th Annual Symposium on Switching Theory and Logical Design (1963) 3–16.
C.A. Petri, Kommunikation mit Automaten. Ph.D. thesis, Rheinisch-Westfälisches Institut für instrumentelle Mathematik an der Universität Bonn (1962).
Rice, H.G., Classes of recursively enumerable sets and their decision problems. Trans. Amer. Math. Soc. 74 (1953) 358–366. Google Scholar
W. Thomas, Automata on infinite objects, in Formal Models and Semantics, edited by J. van Leeuwen. Handbook of Theoret. Comput. Sci. B (1990) 133–191.
Ultes-Nitsche, U., A power-set construction for reducing Büchi automata to non-determinism degree two. Inform. Process. Lett. 101 (2007) 107–111. Google Scholar
Ultes-Nitsche, U. and James, S.St., Improved verification of linear-time properties within fairness – weakly continuation-closed behaviour abstractions computed from trace reductions. Software Testing, Verification and Reliability 13 (2003) 241–255. Google Scholar
M.Y. Vardi and P. Wolper, An automata-theoretic approach to automatic program verification, in Proc. of the 1st Symposium on Logic in Computer Science. Cambridge (1986).
Vardi, M.Y. and Wolper, P., Reasoning about infinite computations. Inform. Comput. 115 (1994) 1–37. Google Scholar