A strict border for the decidability of E-unification for recursive functions

Faßbender, Heinz; Maneth, Sebastian

doi:10.1007/3-540-61735-3_13

Cited by 5 publications

(3 citation statements)

References 21 publications

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“…Unfortunately, their procedure does not represent the set of solutions, and does not terminate for an example like {s(x) + y --, s(x + y), 0 + y --, y} because of the superposition of s(x) with s(x + y). In [4] H. Fafibender and S. Maneth give a decision procedure for unifiability, without representing the set of solutions. But they need very strong restrictions : only one function can be defined and every constructor (as well as the function) is monadic.…”

Section: Related Decidability Results and Conclusionmentioning

confidence: 99%

E-unification by means of tree tuple synchronized grammars

Limet

Réty

1997

TAPSOFT '97: Theory and Practice of Software Development

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The goat of this paper is both to give a E-unification procedure that always terminates, and to decide unifiability. For this, we assume that the equational theory is specified by a confluent and constructor-based rewrite system, and that four additional restrictions are satisfied. We give a procedure that represents the (possibly infinite) set of solutions thanks to a new kind of grammar, called tree tuple synchronized gi.~mmar, and that can decide unifiability thanks to an emptiness test. Moreover we show that if only three of the four additional restrictions are satisfied then unifiability is undecidable.

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Section: Related Decidability Results and Conclusionmentioning

confidence: 99%

E-unification by means of tree tuple synchronized grammars

Limet

Réty

1997

TAPSOFT '97: Theory and Practice of Software Development

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“…For typechecking, the output type is defined as follows. [12] top-down tree transducer [13] to obtain Fibonacci numbers. Given a forest representing n, fib transforms into an output forest representing the n-th Fibonacci number.…”

Section: Appt Appfmentioning

confidence: 99%

Towards Practical Typechecking for Macro Forest Transducers

Abe

Nakano

2017

Journal of Information Processing

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Macro tree transducers (MTTs) and macro forest transducers (MFTs) have been used as good models of tree-structured data transformations such as XML transformations. Typechecking of transformations in these models is performed to verify if any tree of an input type is always transformed into a tree of an output type, which is useful for validating XML transformations against given XML schemata. In typechecking problems for MTTs and MFTs, each "type" is usually given by a tree automaton. A naive implementation of a typechecking algorithm is very inefficient because its time complexity is beyond exponential to the number of states of tree automata, and a large number of equivalence checking operations over finite maps are required. For typechecking of MTTs, Frisch and Hosoya proposed an efficient and practical algorithm by using alternating tree automata as an internal representation of types and reducing the problem to satisfiability checking over first-order logic formulae. In this paper, we extend their typechecking method to apply it to MFTs that are more expressive than MTTs. Our implementation of the proposed method shows that it performs typechecking for relatively simple cases in a reasonable time.

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“…In the undecidability proof for right-ground systems Oyamaguchi used rewrite rules with non-linear variable occurrences at di erent depth. Fassbender & Maneth (1996) investigate decidability of E-uni cation in theories induced by TRS called top-down tree transducers. Syntactic restrictions based on separated function and constructor alphabets are assumed.…”

Section: Limitationsmentioning

confidence: 99%

Unification in extensions of shallow equational theories

Jacquemard

Meyer

Weidenbach

1998

Rewriting Techniques and Applications

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Abstract. We s h o w that uni cation in certain extensions of shallow equational theories is decidable. Our extensions generalize the known classes of shallow or standard equational theories. In order to prove d ecidability of uni cation in the extensions, a class of Horn clause sets called sorted shallow equational theories is introduced. This class is a natural extension of tree automata with equality constraints between brother subterms as well as shallow sort theories. We s h o w that saturation under sorted superposition is e ective on sorted shallow equational theories. So called semi-linear equational theories can be e ectively transformed into equivalent sorted shallow equational theories and generalize the classes of shallow and standard equational theories.

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A strict border for the decidability of E-unification for recursive functions

Cited by 5 publications

References 21 publications

E-unification by means of tree tuple synchronized grammars

E-unification by means of tree tuple synchronized grammars

Towards Practical Typechecking for Macro Forest Transducers

Unification in extensions of shallow equational theories

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