Results 1 
3 of
3
Solving Classes of Set Constraints with Tree Automata
 Proceedings of the Third International Conference on Principles and Practice of Constraint Programming  CP97, volume 1330 of LNCS
, 1997
"... . Set constraints is a suitable formalism for static analysis of programs. However, it is known that the complexity of set constraint problems in the most general cases is very high (NEXPTIMEcompleteness of the satisfiability test). Lots of works are involved in finding more tractable subclasses. I ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
(Show Context)
. Set constraints is a suitable formalism for static analysis of programs. However, it is known that the complexity of set constraint problems in the most general cases is very high (NEXPTIMEcompleteness of the satisfiability test). Lots of works are involved in finding more tractable subclasses. In this paper, we investigate two classes of set constraints shown to be useful for program analysis: the first one is an extension of definite set constraints including the main feature of quantified set expressions. We will show that the satisfiability problem for this class is EXPTIME complete. The second one concerns constraints of the form X ` exp, where exp is built with function symbols, the intersection and union connectives and projection operators. The dual aspects of those two classes allows to find a common approach for solving both of them. This approach uses as basic tool tree automata, which are suitable both for computation and representing the solution of those solving prob...
Ordering Constraints over Feature Trees
, 1999
"... Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
(Show Context)
Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular record descriptions. We introduce the constraint system FT of ordering constraints interpreted over feature trees. Under the view that feature trees represent symbolic information, the relation corresponds to the information ordering ("carries less information than"). We present two algorithms in cubic time, one for the satisfiability problem and one for the entailment problem of FT . We show that FT has the independence property. We are thus able to handle negative conjuncts via entailment and obtain a cubic algorithm that decides the satisfiability of conjunctions of positive and negated ordering constraints over feature trees. Furthermore, we reduce the satisfiability problem of Dorre's weak subsumption constraints to the satisfiability problem of FT and improve the complexity bound for solving weak subsumption constraints from O(n^5) to O(n³).
Ordering Constraints over Feature Trees Expressed in Secondorder Monadic Logic
 Information and Computation
, 1998
"... The language FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. While the firstorder theory of FT is well understood, only few decidability results are known for the firstorder theory of FT . We introduc ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
The language FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. While the firstorder theory of FT is well understood, only few decidability results are known for the firstorder theory of FT . We introduce a new method for proving the decidability of fragments of the firstorder theory of FT . This method is based on reduction to second order monadic logic that is decidable according to Rabin's famous tree theorem. The method applies to any fragment of the firstorder theory of FT for which one can change the model towards sufficiently labeled feature trees  a class of trees that we introduce. As we show, the first ordertheory of ordering constraints over sufficiently labeled feature trees is equivalent to secondorder monadic logic (S2S for infinite and WS2S for finite feature trees). We apply our method for proving that entailment of FT with existential quantifiers j 1 j=9x 1 : : :9x n j 2 is decidable. Previous results were restricted to entailment without existential quantifiers which can be solved in cubic time. Meanwhile, entailment with existential quantifiers has been shown PSPACEcomplete (for finite and infinite feature trees respectively).