Program schemes, recursion schemes, and formal languages

Garland, Stephen J.; Luckham, David C.

doi:10.1016/s0022-0000(73)80040-6

Cited by 87 publications

(21 citation statements)

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“…Decidability follows from the result of Sénizergues on the decidability of the language-equivalence problem for DPDAs [20]. The problems of DPDA equivalence and (strong) equivalence of monadic recursion schemes are interreducible, as shown in [8] and [7]. The primitive recursive upper bound follows from the result of Stirling [25], which is a strengthening of the decidability result for DPDA equivalence.…”

Section: The Simple Implicational Theorymentioning

confidence: 92%

“…The (strong) equivalence problem for program schemes is checking whether two schemes denote the same partial function under every possible interpretation of the atomic actions and predicates. Garland and Luckham showed in [8] (page 132, Theorem 2.10, part (b)) that the equivalence of monadic recursion schemes can be reduced to the equivalence problem for deterministic context-free grammars (these grammars correspond to DPDAs). Moreover, Friedman showed in [7] the converse, namely, that DPDA equivalence can be reduced to monadic recursion scheme equivalence.…”

Section: Introductionmentioning

confidence: 99%

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On the Hoare theory of monadic recursion schemes

Mamouras

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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The equational theory of monadic recursion schemes is known to be decidable by the result of Sénizergues on the decidability of the problem of DPDA equivalence. In order to capture some properties of the domain of computation, we augment equations with certain hypotheses. This preserves the decidability of the theory, which we call simple implicational theory. The asymptotically fastest algorithm known for deciding the equational theory, and also for deciding the simple implicational theory, has running time that is non-elementary. We therefore consider a restriction of the properties about schemes to check: instead of arbitrary equations f ≡ g between schemes, we focus on propositional Hoare assertions {p}f {q}, where f is a scheme and p, q are tests. Such Hoare assertions have a straightforward encoding as equations. We investigate the Hoare theory of monadic recursion schemes, that is, the set of valid implications whose conclusions are Hoare assertions and whose premises are of a certain simple form. We present a sound and complete Hoare-style calculus for this theory. We also show that the Hoare theory can be decided in exponential time, and that it is complete for this class.

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Section: The Simple Implicational Theorymentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

On the Hoare theory of monadic recursion schemes

Mamouras

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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show abstract

“…Similar to program schemes are Garland and Luckham's recursion schemes [32], which are modeled on mutually independent recursive definitions of functions. Garland and Luckham show here that certain classes of recursion schemes are translatable into program schemes.…”

Section: Program Schemes and Interpretationsmentioning

confidence: 99%

A survey of state vectors

Maurer

2008

Computer Science Review

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“…The equivalence problem for linear unary recursive program schemas [8] with invertible operators is reduced to the equivalence proboem for determined reading ~TI-transformators with a free output group. …”

Section: /~[(Gf~)c] ~(/F)c~ (D#2 !C (Z~ (/3)c~ ) E ~(~ )mentioning

confidence: 99%

Quasirelations in a free group and transformator equivalence problems

Lisovik¹

1986

Algebra and Logic

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Program schemes, recursion schemes, and formal languages

Cited by 87 publications

References 3 publications

On the Hoare theory of monadic recursion schemes

On the Hoare theory of monadic recursion schemes

A survey of state vectors

Quasirelations in a free group and transformator equivalence problems

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