We discuss the technique for testing the equivalence of two deterministic automata by constructing a language that matches the computations of two equivalent automata on the same input word. Specifically, we propose to use HDTOL languages that are powerful enough to match computations of many equivalent deterministic multitape automata, and at the same time, have nice decidable properties. Using this new technique of HDTOL matching, we show that the inclusion problem between an arbitrary deterministic multitape automaton and a simple one is decidable in both directions. Further, we show that the equivalence for a restricted class of transducers based on deterministic multitape automata is decidable.
KeywordsInformation System Operating System Data Structure Communication Network Information Theory
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- 1.Berstel, J.: Transductions and Context-Free Languages. Stuttgart: Teubner 1979Google Scholar
- 2.Bird, M.: The equivalence problem for deterministic two-tape automata. J. Comput. Syst. Sci. 7, 218–236 (1973)Google Scholar
- 3.Culik II, K., Karhumäki, J.: The equivalence of finite valued transducers (on HDTOL languages) is decidable. Theor. Comput. Sci. 47, 71–84 (1986)Google Scholar
- 4.Culik II, K., Karhumäki, J.: Loops in automata and HDTOL relations. RAIRO, Inf. Théor. Appl. (to appear)Google Scholar
- 5.Culik II, K., Salomaa, A.: On the decidability of morphic equivalence for languages. J. Comput. Syst. Sci. 17, 163–175 (1978)Google Scholar
- 6.Ginsburg, S.: The Mathematical Theory of Context-Free Languages. New York: McGraw Hill 1966Google Scholar
- 7.Harrison, M.: Introduction to Formal Language Theory. Reading: Addison-Wesley 1978Google Scholar
- 8.Kinber, E.: The inclusion problem for some classes of deterministic multitape automata. Theor. Comput. Sci. 26, 1–24 (1983)Google Scholar
- 9.Lewis, H.R.: A new decidability problem with applications. Proceedings of 18th FOCS Conference, pp. 62–73 (1979)Google Scholar
- 10.Rabin, M., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3, 114–125 (1959)Google Scholar
- 11.Rozenberg, G., Salomaa, A.: The Mathematical Theory of L Systems. New York: Academic Press 1980Google Scholar
- 12.Valiant, L.G.: The equivalence problem for deterministic finite-turn pushdown automata. Inf. Control 25, 123–133 (1974)Google Scholar