Abstract
Two schema problems from the 1970s are examined, monadic recursion schemes and first-order recursion schemas. Research on these problems halted because they were shown to be equivalent to the problem of decidability of language equivalence between DPDA (deterministic pushdown automata). Recently a decidability proof for equivalence of DPDA was given by Sénizergues [10, 11], which therefore also solves the schema problems. However Sénizergues proof is quite formidable. A simplification of the proof was presented by the author [13] using ideas from concurrency theory (for showing decidability of bismilarity [9, 12]) and crucial insights from Sénizergues’s intricate proof.
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References
Courcelle, B. 1978. A representation of trees by languages I, Theoretical Computer Science, 6, 255–279.
Courcelle, B. 1978. A representation of trees by languages II, Theoretical Computer Science, 7, 25–55.
Damm W, 1977. Languages defined by higher type program schemes, Lecture Notes in Computer Science, 52, 164–179.
Damm W, 1979. An algebraic extension of the Chomsky-hierarchy. Lecture Notes in Computer Science, 74, 266–276.
Friedman, E. 1977. Equivalence problems for deterministic context-free languages and monadic recursion schemes. Journal of Computer and System Sciences, 14, 344-359.
Garland, S., and Luckham, D. 1973. Program schemes, recursion schemes, and formal languages. Journal of Computer and System Sciences, 7, 119–160.
Harrison, M. 1978. Introduction to Formal Language Theory, Addison-Wesley.
Harrison, M., and Havel, I. 1973. Strict deterministic grammars. Journal of Computer and System Sciences, 7, 237–277.
Hüttel, H., and Stirling, C. 1991. Actions speak louder than words: proving bisimilarity for context free processes. Proceedings 6th Annual Symposium on Logic in Computer Science, IEEE Computer Science Press, 376–386.
Sénizergues, G. 1997. The equivalence problem for deterministic pushdown automata is decidable. Lecture Notes in Computer Science, 1256, 671–681.
Sénizergues, G. 1998. L(A) = L(B)? Tech. Report LaBRI, Université Bordeaux I, pp. 1–166. (To appear in Theoretical Computer Science.
Stirling, C. (1998). Decidability of bisimulation equivalence for normed pushdown processes. Theoretical Computer Science, 195, 113–131.
Stirling, C. 1999. Decidability of DPDA equivalence. Tech. Report LFCS-99-411, University of Edinburgh, pp. 1–25. (To appear in Theoretical Computer Science.
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Stirling, C. (2000). Schema Revisited. In: Clote, P.G., Schwichtenberg, H. (eds) Computer Science Logic. CSL 2000. Lecture Notes in Computer Science, vol 1862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44622-2_7
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DOI: https://doi.org/10.1007/3-540-44622-2_7
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