Typical Paths of a Graph

  • Authors:

  • Cewei Cui;Zhe Dang;Thomas R. Fischer

  • Affiliations:

  • School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164, USA. ccui@eecs.wsu.edu/ zdang@eecs.wsu.edu/ fischer@eecs.wsu.edu;(Correspd.) School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164, USA. ccui@eecs.wsu.edu/ zdang@eecs.wsu.edu/ fischer@eecs.wsu.edu;School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164, USA. ccui@eecs.wsu.edu/ zdang@eecs.wsu.edu/ fischer@eecs.wsu.edu

  • Venue:
  • Fundamenta Informaticae - Theory that Counts: To Oscar Ibarra on His 70th Birthday
  • Year:
  • 2011

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Abstract

We introduce (finite and infinite) typical paths of a graph and prove that the typical paths carry all information with probability 1, asymptotically. An automata-theoretic characterization of the typical paths is shown: finite typical paths can be accepted by reversal-bounded multicounter automata and infinite typical paths can be accepted by counting Büchi automata (a generalization of reversal-bounded multicounter automata running on ω-words). We take a statechart example to show how to generate typical paths from a graph using SPIN model checker. The results are useful in automata theory since one can identify an information-concentrated-core of a regular language such that only words in the information-concentrated-core carry nontrivial information. When the graph is used to specify the system under test, the results are also useful in software testing by providing an information-theoretic approach to select test cases that carry nontrivial information of the system specification.