Abstract
We explore the boundaries between decidability and undecidability of the containment and equivalence problems for restricted classes of nondeterministic generalized sequential machines (NGSMs), nondeterministic finite transducers (NFTs), nondeterministic pushdown transducers (NPDTs), and linear context-free grammars (LCFGs). We believe that our results are the sharpest known to date concerning these devices.
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References
Baker, B., Book, R.: Reversal-bounded multipushdown machines. J. Comput. Syst. Sci. 8, 315–322 (1974)
Culik, K., Karhumaki, J.: The equivalence of finite valued transducers (on HDTOL languages) is decidable. Theoret. Comput. Sci. 47, 71–84 (1986)
Griffiths, T.: The unsolvability of the equivalence problem for Λ-free nondeterministic generalized sequential machines. J. Assoc. Comput. Mach. 15, 409–413 (1968)
Gurari, E., Ibarra, O.H.: A note on finite-valued and finitely ambiguous transducers. Math. Systems Theory 16, 61–66 (1983)
Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. J. Assoc. Comput. Mach. 25, 116–133 (1978)
Ibarra, O.H.: The unsolvability of the equivalence problem for ε-free NGSM’s with unary input (output) alphabet and applications. SIAM J. Computing 7, 524–532 (1978)
Minsky, M.: Recursive unsolvability of Post’s problem of Tag and other topics in the theory of Turing machines, Ann. of Math. 74, 437–455 (1961)
Weber, A.: On the valuedness of finite transducers. Acta Inform. 27, 749–780 (1990)
Weber, A.: Decomposing finite-valued transducers and deciding their equivalence. SIAM. J. on Computing 22, 175–202 (1993)
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Ibarra, O.H. (2011). On the Containment and Equivalence Problems for GSMs, Transducers, and Linear CFGs. In: Bouchou-Markhoff, B., Caron, P., Champarnaud, JM., Maurel, D. (eds) Implementation and Application of Automata. CIAA 2011. Lecture Notes in Computer Science, vol 6807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22256-6_18
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DOI: https://doi.org/10.1007/978-3-642-22256-6_18
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