Manfred Schmidt-Schau. Decidability of bounded second order unification. Technical Report Frank-report-11, FB Informatik, J.W. Goethe-Universitat Frankfurt am Main, 1999. submitted for publication.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....: b) Y (X(a; p : a) q : X(a; p : a) b; r : b) nondeterministically, for any possible choice of p; q; r k satisfying the bound. The converse reduction does not seem easy to find. The bounded second order unification problem has recently been proved decidable [SS99b]. The relationship between context unification and word unification [Mak77] was originally suggested in [Lev96] In [SSS98] it is proved that the exponent of periodicity lemma also holds for context unification. We can easily reduce word unification to context unification by encoding any word ....

M. Schmidt-Schau. Decidability of bounded second-order unification. Technical Report Frank-report-11, FB Informatik, J.W. Goethe Universitat Frankfurt, 1999.

....variables (depending on the arity of the variable) Second, there is no limitation on the number of occurrences of a given bound variable in the substitution term, and in particular this number may be zero. This second property makes an important difference to context unification. A recent result [23] shows that second order unification becomes decidable if an upper bound on the number of occurrences of a given bound variable in the substitution term is fixed. If context unification would turn out to be decidable, the latter result would be a simple consequence. It is known that second order ....

M. Schmidt-Schau. Decidability of bounded second order unification. Draft, Fachbereich Informatik, J.W. Goethe-Universitat Frankfurt, Germany, 1998. 31

....neither the use of bindings. The restriction of using unary context variables is not a real restriction because we can replace binary (similarly for n ary) variables like F (t 1 ; t 2 ) by F 0 (f(F 1 (t 1 ) F 2 (t 2 ) introducing a conjectured constant symbol f (see Subsection 3. 2 and [12]) However, the equivalence of both problems was never formally proved. The naive attempt to reduce LSOU to CU by replacing bound variables by new constant symbols does not work. This is because we have to ensure that substitutions avoid variable capture. For instance, the following LSOU problem ....

....unification is reducible to n ary context unification plus tree regular constraints. 3.2 Reducing n ary context unification to (1 ary) context unification In this subsection we reduce the n ary CU problem to the (1 ary) CU problem. The same main ideas are also used in other previous papers, like [12]. Given an 7 n ary context unification problem S over a signature Sigma , if Sigma does not contain an n ary constant with n 2 and a first order constant, we enlarge it with them. We construct a new context unification problem S 0 by iteratively applying the following rule, until all ....

M. Schmidt-Schau. Decidability of bounded second-order unification. Technical Report Frank-report-11, FB Informatik, J.W. Goethe Universitat Frankfurt, 1999.

.... variables [SSS99] or if the context unification problems are stratified [SS99b] Satisfiability in a logical theory of context unification is undecidable [NPR97,Vor98] A decidable restriction of second order unification similar in spirit to context unification is bounded second order unification [SS99a], where second order variables represent terms with a number of holes that is bounded by some preselected number. Applications of context unification are for example in computational linguistics [NPR97] and of (stratified) context unification in equational unification [SS98] Recently it was ....

....the depth of SO cycles implies a complexity estimate of stratified context unification. Proving better complexity estimations of stratified context unification or proving an upper bound for the depth of SO cycles is left for future work. The decision algorithm for bounded second order unification [SS99a] is very similar to the decision algorithm for stratified context unification. The methods developed in this paper may be used in an estimation of its complexity. Perhaps the tools in this paper help in computing an upper bound for the complexity of D unification [SS98] however, this would ....

Manfred Schmidt-Schau. Decidability of bounded second order unification. Technical Report Frank-report-11, FB Informatik, J.W. Goethe-Universitat Frankfurt am Main, 1999. submitted for publication.

....variables, but there are at most two context variables [SSS99] In this paper we show that another fragment, namely stratified context unification, is decidable. A decidable 1 restriction of second order unification similar in spirit to context unification is bounded second order unification [SS99], where second order variables represent terms with zero or one hole. Satisfiability in a logical theory of context unification is undecidable [Vor98] Applications of context unification are for example in computational linguistics [NPR97] and of (stratified) context unification in equational ....

Manfred Schmidt-Schau. Decidability of bounded second order unification. Technical Report Frank-report-11, FB Informatik, J.W. Goethe-Universitat Frankfurt am Main, 1999.

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