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k-counting automata

  • Joël Allred (a1) and Ulrich Ultes-Nitsche (a1)


In this paper, we define k-counting automata as recognizers for ω-languages, i.e. languages of infinite words. We prove that the class of ω-languages they recognize is a proper extension of the ω-regular languages. In addition we prove that languages recognized by k-counting automata are closed under Boolean operations. It remains an open problem whether or not emptiness is decidable for k-counting automata. However, we conjecture strongly that it is decidable and give formal reasons why we believe so.



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[1] Alpern, B. and Schneider, F.B., Defining liveness. Inf. Process. Lett. 21 (1985) 181185.
[2] 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.
[3] 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 Unpublished manuscript.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.
[4] 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.
[5] 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.
[6] Fernau, H. and Stiebe, R., Blind counter automata on ω-words. Fundam. Inform. 83 (2008) 5164.
[7] Fischer, P.C., Turing machines with restricted memory access. Inf. Control 9 (1966) 364379.
[8] Hashiguchi, K., Algorithms for determining relative star height and star height. Inf. Comput. 78 (1988) 124169.
[9] J.E. Hopcroft, R. Motwani and J.D. Ullman, Introduction to Automata Theory, Languages and Computation. Addison Wesley, Pearson Education (2006).
[10] Karp, R.M. and Miller, R.E., Parallel program schemata. J. Comput. Syst. Sci. 3 (1969) 147195.
[11] R.P. Kurshan, Computer-Aided Verification of Coordinating Processes, 1st edition. Princeton University Press, Princeton, New Jersey (1994).
[12] E.W. Mayr, An algorithm for the general petri net reachability problem, in Proc of the 13th Annual ACM Symposium on Theory of Computing, STOC81. New York, USA, ACM (1981) 238–246.
[13] McNaughton, R., Testing and generating infinite sequences by a finite automaton. Inf. Control 9 (1966) 521530.
[14] Minsky, M.L., Recursive unsolvability of post’s problem of “tag” and other topics in theory of turing machines. Ann. Math. 74 (1961) 437455.
[15] 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.
[16] C.A. Petri, Kommunikation mit Automaten. Ph.D. thesis, Rheinisch-Westfälisches Institut für instrumentelle Mathematik an der Universität Bonn (1962).
[17] Rice, H.G., Classes of recursively enumerable sets and their decision problems. Trans. Amer. Math. Soc. 74 (1953) 358366.
[18] 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.
[19] Ultes-Nitsche, U., A power-set construction for reducing Büchi automata to non-determinism degree two. Inform. Process. Lett. 101 (2007) 107111.
[20] 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) 241255.
[21] 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).
[22] Vardi, M.Y. and Wolper, P., Reasoning about infinite computations. Inform. Comput. 115 (1994) 137.



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