Abstract
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 computations of two simple automata can be HDTOL matched on their common domain. This implies that the equivalence problem for transducers based on simple automata is decidable. The latter result is the best possible since the problem is undecidable even for transducers based on automata with parallel loops.
Reported research was supported by the National Sciences Foundation Grant CCR-8702752.
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References
J. Berstel, Transductions and Context-Free Languages, Teubner, Stuttgart, 1979.
M. Bird, The equivalence problem for deterministic two-tape automata, J. Comput. Sci. 7 (1973) 218–236.
K. Culik II, A purely homomorphic characterization of recursively enumerable sets, J. Assoc. Comput. Mach. 6 (1979) 345–350.
K. Culik II and J. Karhumäki, Systems of equations over a free monoid and Ehrenfeucht's conjecture, Discrete Math. 43 (1983) 139–153.
K. Culik II and J. Karhumäki, The equivalence of finite valued transducers (on HDTOL languages) is decidable, Theoret. Comput. Sci. 47 (1986) 71–84.
K. Culik II and J. Karhumäki, Systems of equations over a finitely generated free monoid having an effectively findable equivalent finite subsystem, in: H.Jurgensen, G.Lallement and H.Weinert (eds), Semigroups Theory and Applications, Oberwolfach 1986, Lecture Notes in Mathematics 1320, pp. 18–27 (Springer, 1988).
K. Culik II and J. Karhumäki, Loops in automata and HDTOL relations, Technical Report TR88003, USC (1988).
K. Culik II and J. Karhumäki, HDTOL matching of computations of multitape automata, Technical Report TR88004, USC (1988).
K. Culik II and A. Salomaa, On the decidability of morphic equivalence for languages, J. Comput. System Sci. 17 (1978) 163–175.
M. Harrison, Introduction to Formal Language Theory, Addison-Wesley, Reading, 1978.
E. Kinber, The inclusion problem for some classes of deterministic multitape automata, Theoret. Comput. Sci. 26 (1983) 1–24.
H. R. Lewis, A new decidability problem with applications, Proceedings of 18th FOCS Conference (1979) 62–73.
M. Rabin and D. Scott, Finite automata and their decision problems, IBM J. Res. Develop. 3 (1959) 114–125.
G. Rozenberg and A. Salomaa, The Mathematical Theory of L Systems, Academic Press, New York, 1980.
L. G. Valiant, The equivalence problem for deterministic finite-turn pushdown automata, Inform. Control 25 (1974) 123–133.
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© 1989 Springer-Verlag Berlin Heidelberg
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Culik, K., Karhumäki, J. (1989). On the equivalence problem for deterministic multitape automata and transducers. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029008
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DOI: https://doi.org/10.1007/BFb0029008
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