H. COMON. Unification et Disunification. Th'eorie et Applications. PhD thesis, INPG, Grenoble, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....will be called G formulae in this paper. Obviously, G formulae have a greater expressive power than equational formulae. Hence, this representation is strictly more powerful than the one we use in our previous work [7, 8, 2] Moreover the validity problem for G formulae is known to be decidable [11, 14]. The advantages of our approach are numerous. Most problems about models can be solved very easily by using existing constraints solving algorithms. For example we show how the evaluation problem, i.e. the problem of finding the truth value of a formula in a given interpretation, or the ....

....the use of G formulae into our model building method RAMC. 2.3. Regular tree grammars Regular tree grammars are a particular case of context free tree grammars. Intuitively, they behave exactly as regular grammars for strings. Regular tree grammars have been widely studied by several authors [20, 11, 14]. The languages generated by regular tree grammars are also recognized by finite tree automata. This fact implies the closure properties under the usual boolean transformations (union, intersection and complement) In this section we define the notion of regular tree grammars and recall some of ....

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H. COMON. Unification et Disunification. Th'eorie et Applications. PhD thesis, INPG, Grenoble, 1988.

....P and is noted Sol(P) An equational formula X such that Sol(X ) resp. Sol( X ) is said to be unsatisfiable (resp. valid) The validity problem of equational formulae is known to be decidable and algorithms have been given in order to find the solution of a given equational formula (see [11, 10] and also [21, 17, 20] 2.2. Constrained formulae The set of constrained formula (of c formula for short) is inductively defined as the least set containing AA 0 , AA 0 , A, 8x : X:A, 9x : X:A, P (t 1 ; t n ) where A; A 0 are c formulae, t i (1 i n) are terms, P 2 Omega Gamma ....

H. Comon. Unification et Disunification. Th'eorie et Applications. PhD thesis, INPG, Grenoble, 1988. In french.

....formula without quantifiers. A substitution oe is said to be a solution of a problem P iff Poe is valid in the empty theory (i.e. in the Herbrand universe) Equational problems have a lot of interesting application, for example in inductive theorem proving, specification, model building: [5, 4]. In [5, 6] an algorithm has been proposed to find the solutions of any equational problem. This algorithm is given as a set of rules, allowing to transform any equational problem into a set of problems in solved form . This algorithm can be very easely implemented by using the system Disc ....

....without quantifiers. A substitution oe is said to be a solution of a problem P iff Poe is valid in the empty theory (i.e. in the Herbrand universe) Equational problems have a lot of interesting application, for example in inductive theorem proving, specification, model building: 5, 4] In [5, 6] an algorithm has been proposed to find the solutions of any equational problem. This algorithm is given as a set of rules, allowing to transform any equational problem into a set of problems in solved form . This algorithm can be very easely implemented by using the system Disc Atinf . First ....

H. COMON. Unification et Disunification. Th'eorie et Applications. PhD thesis, INPG, Grenoble, 1988.

....An equational problem P is in definition with constraints iff P is either , or , or P is 9w: V m j=1 x j = s j ] V k i=1 x 0 i 6= s 0 i ] where x j 62 w, each x j appears only once in P and each x 0 i is syntactically different from s 0 i . In [Comon, Lescanne, 1989] see also [Comon, 1988]) a set of rules is proposed in order to eliminate parameters from a problem P and to transform P into a union of problems 6 N. Peltier in solved form definition with constraints , from which the solutions of the problem can easily be extracted. This system is sound (i.e. all the solutions are ....

Comon, 1988 Comon H. (1988). Unification et Disunification. Th'eorie et Applications. PhD thesis, INPG, Grenoble, 1988.

.... free algebra of an equational specification (see Comon (1991) and Burckert Schmidt Schau (1989) The first example (A) treats the decision problem for the theory of ground term algebras modulo the axioms of associativity and commutativity (AC for short) and has been given as an open problem in Comon (1988). In this paper the existential fragment has been shown decidable thus extending the results for AC unification (Stickel (1981) Livesey Siekmann (1976) Fages (1987) and Kirchner (1985) for arbitrary additional free function symbols) This example shows that equational problems may be ....

....undecidability result to the case of infinite trees. The decidability of the the existential fragment of the theory of finite and infinite trees with the subtree relation was shown in Tulipani (1993) The question of decidability of the theory of a total simplification ordering has been posed in Comon (1988). The decidability of the existential fragment of a total lexicographic path ordering (lpo for short) is shown in Comon (1990) the analogous result for a total recursive path ordering has been given in Jouannaud Okada (1991) We prove in Example (C) the undecidability of the Sigma 4 fragment ....

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Comon, H. (1988). Unification et Disunification. Th'eorie et Applications. PhD thesis, Institut National Polytechnique de Grenoble, Grenoble, France.

....when the language is empty, the naive algorithm derived from the pumping lemma consists in checking the membership of all trees of depth smaller than the bound. When the language is empty, this means that the bound is reached indeed. That is why some of us tried to design cleaning algorithms [5]. The idea is roughly to use the grammar associated with the automaton, trying to generate some tree in the language. The main difference with the other method is that, during the generation process, we cut the search branches for which we know in advance that there is no hope to find a tree in ....

H. Comon. Unification et disunification. Th'eorie et applications. PhD thesis, I.N.P.Grenoble, 1988.

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