An Architecture for Cooperating Constraint Solvers on Reals

In this paper we introduce a cooperative scheme for solving systems of constraints over the reals. First, we informally show how an appropriate combination of symbolic and numeric solvers makes it possible to solve problems that none of these solvers can tackle alone. Then, we specify a cooperative architecture which allows to use concurrently heterogeneous solvers when handling constraints over the reals. This architecture is based upon agents that communicate via asynchronous message passing. Agent are synchronized when a failure or a success occurs. Disjunctive constraints are handled by backtracking. Operational semantics and terminating conditions of such systems are discussed. Message processing is detailed for both the general case where several non-deterministic solvers are involved in the cooperation, and for more specialized architectures.

[1]  Francesca Rossi,et al.  CC Programs with both In- and Non-determinism: A Concurrent Semantics , 1994, PPCP.

[2]  Michael J. Maher,et al.  Constraint Logic Programming: A Survey , 1994, J. Log. Program..

[3]  Keith O. Geddes,et al.  Algorithms for computer algebra , 1992 .

[4]  Bruce W. Char,et al.  Maple V Language Reference Manual , 1993, Springer US.

[5]  Timothy W. Finin,et al.  A semantics approach for KQML—a general purpose communication language for software agents , 1994, CIKM '94.

[6]  Pascal Van Hentenryck,et al.  CLP(Intervals) Revisited , 1994, ILPS.

[7]  Carl Hewitt,et al.  Viewing Control Structures as Patterns of Passing Messages , 1977, Artif. Intell..

[8]  B. Buchberger,et al.  Grobner Bases : An Algorithmic Method in Polynomial Ideal Theory , 1985 .

[9]  M. H. van Emden,et al.  Adapting CLP to Floating-Point Arithmetic , 1992, FGCS.

[10]  Hoon Hong.  RISC-CLP(Real): Logic Programming with Non-linear Constraints over the Reals , 1991, WCLP.

[11]  David L. Waltz,et al.  Generating Semantic Descriptions From Drawings of Scenes With Shadows , 1972 .

[12]  Tim Finin,et al.  KQML - A Language and Protocol for Knowledge and Information Exchange , 1994 .

[13]  Frank S. de Boer,et al.  Non-monotonic Concurrent Constraint Programming , 1993, ILPS.

[14]  Frank S. de Boer,et al.  On the Semantics of Concurrent Constraint Programming , 1992, ALPUK.

[15]  Olivier Lhomme,et al.  Consistency Techniques for Numeric CSPs , 1993, IJCAI.

[16]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[17]  Greg Nelson,et al.  Simplification by Cooperating Decision Procedures , 1979, TOPL.

[18]  Gul A. Agha,et al.  ACTORS - a model of concurrent computation in distributed systems , 1985, MIT Press series in artificial intelligence.

[19]  Barr and Feigenbaum Edward A. Avron,et al.  The Handbook of Artificial Intelligence , 1981 .

[20]  Henri Beringer,et al.  Combinatorial Problem Solving in Constraint Logic Programming with Cooperating Solvers , 1995, Logic Programming: Formal Methods and Practical Applications.

[21]  Prakash Panangaden,et al.  The semantic foundations of concurrent constraint programming , 1991, POPL '91.

[22]  Gilles Pesant,et al.  QUAD-CLP(R): Adding the Power of Quadratic Constraints , 1994, PPCP.

[23]  Kenneth M. Kahn,et al.  Janus: A step towards distributed constraint programming , 1990, NACLP.

[24]  Roland H. C. Yap,et al.  The CLP( R ) language and system , 1992, TOPL.

[25]  Vijay A. Saraswat,et al.  Concurrent constraint programming , 1989, POPL '90.

[26]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[27]  Michel Rueher.  A first exploration of PrologIII's capabilities , 1993, Softw. Pract. Exp..

[28]  Alain Colmerauer,et al.  An introduction to Prolog III , 1989, CACM.

[29]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[30]  George E. Collins,et al.  Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975, Automata Theory and Formal Languages.