Solving Linear, Min and Max Constraint Systems Using CLP Based on Relational Interval Arithmetic

Many real problems can be treated as Constraint Satisfaction Problems (CSPs), a type of problem for which efficient tools have been developed. Computing the maximum timing separations between the events of a timing specification falls into this category. CLP (BNR) is a constraint logic programming language which seems well suited to the problem, allowing to draw from the advantages of both CSPs and Logic Programming. Consistency techniques used for solving general CSPs usually produce approximate answers (partial consistency) and the resolution engine for CLP (BNR) behaves in a similar fashion. However, for some specific timing specifications, we show that global consistency can be achieved using CLP (BNR). The timing specifications we consider are systems of strictly linear constraints, systems of either max-only or min-only constraints, and systems where linear and either max or min constraints intermix.

[1]  Eduard Cerny,et al.  Integrating Behavior and Timing in Executable Specifications , 1993, CHDL.

[2]  Ramon E. Moore.  Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.

[3]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[4]  Marc Gyssens,et al.  A Unifying Framework for Tractable Constraints , 1995, CP.

[5]  Patrick Henry Winston,et al.  The psychology of computer vision , 1976, Pattern Recognit..

[6]  Pascal Van Hentenryck.  Constraint satisfaction in logic programming , 1989, Logic programming.

[7]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

[8]  Rina Dechter,et al.  From Local to Global Consistency , 1990, Artif. Intell..

[9]  Sharad Malik,et al.  Statistical timing analysis of combinational logic circuits , 1993, IEEE Trans. Very Large Scale Integr. Syst..

[10]  Joxan Jaffar,et al.  Constraint logic programming , 1987, POPL '87.

[11]  Gaetano Borriello,et al.  An approach to symbolic timing verification , 1992, [1992] Proceedings 29th ACM/IEEE Design Automation Conference.

[12]  Danny De Schreye,et al.  Implementing a Finite-domain CLP-language on Top of Prolog: a Transformational Approach , 1994, LPAR.

[13]  Farhad Mavaddat,et al.  Consistency and satisfiability of waveform timing specifications , 1991, Networks.

[14]  Anthony Joseph Gahlinger.  Coherence and satisfiability of waveform timing specifications , 1990 .

[15]  Gaetano Borriello,et al.  Interface Timing Verification with Application to Synthesis , 1994, 31st Design Automation Conference.

[16]  Wayne H. Wolf,et al.  Efficient Algorithms for Interface Timing Verification , 1994, EURO-DAC '94.

[17]  David L. Dill,et al.  Algorithms for interface timing verification , 1992, Proceedings 1992 IEEE International Conference on Computer Design: VLSI in Computers & Processors.

[18]  Gaetano Borriello,et al.  An algorithm for exact bounds on the time separation of events in concurrent systems , 1993, Proceedings of 1993 IEEE International Conference on Computer Design ICCD'93.

[19]  G. Goossens,et al.  Specification and analysis of timing constraints in signal transition graphs , 1992, [1992] Proceedings The European Conference on Design Automation.

[20]  André Vellino,et al.  Constraint Arithmetic on Real Intervals , 1993, WCLP.

[21]  Pascal Van Hentenryck,et al.  An Efficient Arc Consistency Algorithm for a Class of CSP Problems , 1991, IJCAI.

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

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

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

[25]  P. Schönemann.  On artificial intelligence , 1985, Behavioral and Brain Sciences.

[26]  William Leler,et al.  Constraint programming languages: their specification and generation , 1988 .

[27]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

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

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