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A New Technique for Reachability of States in Concatenation Automata

  • Sylvie Davies
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10952)

Abstract

We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the concatenation of two languages, and thus in establishing the state complexity of concatenation as an operation. Typically, ad-hoc induction arguments are used to show particular states are reachable in concatenation automata. We prove some results that seem to capture the essence of many of these induction arguments. Using these results, reachability proofs in concatenation automata can often be done more simply and without using induction directly.

Notes

Acknowledgements

I thank Jason Bell, Janusz Brzozowski and the anonymous referees for proofreading and helpful comments. This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871.

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Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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