P. V. Hentenryck, H. Simonis, and M. Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58:113--159, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that test whether a given, partially built reaction mechanism is consistent with a given constraint. A possible approach to this and other constraint satisfaction problems of scientific inference is to draw on parallel work in constraint satisfaction, e.g. constraint logic programming (CLP) [5]. We have previously experimented with the CLP language Prolog III [1] in the context of MECHEM s pathway generator [8] but returned to programming from scratch in Lisp because of the complicated algorithmic nature of the further constraints that were needed to make MECHEM into a competent ....

P. V. Hentenryck, H. Simonis, and M. Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58:113--159, 1992.

....is a very powerful mechanism and it is used to awake delayed constraints or to generate a solution to an already known satisfiable system of constraints. The labeling strategies are critical to the overall efficiency of the solver. A discussion of constraint satisfaction using CLP can be found in [125]. For example, in Prolog the equality: X X Y = 10 results in failure, since in Prolog equality only holds between syntactically identical terms and X is just a variable of no particular type. Using a CLP 65 language however, it is possible to code the semantics of X and Y as being integerlike ....

P. V. Hentenryck, H. Simonis, and M. Dincbas, "Constraint Satisfaction Using Constraint Logic Programming," Artificial Intelligence, vol. 58, pp. 113--159, 1992.

....satisfaction methods (section 2.1) and different kinds of constraint networks (section 2.2) 2.1. Classification of Satisfaction Methods At present there are six prevailing satisfaction methods [4, 8, 9, 10, 21, 22] ignoring the satisfaction methods which are used in Artificial Intelligence [14, 15]) In this section each of these methods will be presented. Propagation of known states (or Local Propagation) is a satisfaction method which propagates the results of constraint satisfaction one by one through the nodes of the constraint network. Propagation of known states is a satisfaction ....

Hentenryck P. van, Simonis H. (1991). DINCBAS M., Constraint Satisfaction using Constraint Logic Programming, tech.rep. CS91-62, Brown 353 University.

....the domain of Y (X) or by the minimum and maximum of Y (X) The domain approximation performs stronger propagation than the interval approximation, but the interval version is more efficient to compute. For a careful examination of domain and interval approximations of constraints see elsewhere [6, 13, 14]. Note that operationally the constraint propagation implemented by the FD constraints may be weaker than what can be performed by a constraint solver for the n ary constraint. Example 2. The constraint X 6= Y can be defined either as X 6= Y : Gamma X in Gamma dom(Y ) Y in Gamma dom(X) ....

M. Dincbas, P. van Hentenryck, and H. Simonis. Constraint Satisfaction using constraint logic programming. In Artifical Intelligence, vol 58, 113-159, 1992.

....is a very powerful mechanism and it is used to awake delayed constraints or to generate a solution to an already known satisfiable system of constraints. The labeling strategies are critical to the overall efficiency of the solver. A discussion of constraint satisfaction using CLP can be found in [115]. For example, in Prolog the equality: X X Y = 10 results in failure, since in Prolog equality only holds between syntactically identical terms and X is just a variable of no particular type. Using a CLP language however, it is possible to code the semantic of X and Y as being integerlike and ....

P. V. Hentenryck, H. Simonis, and M. Dincbas, "Constraint Satisfaction Using Constraint Logic Programming," Artificial Intelligence, vol. 58, pp. 113--159, 1992.

....familiar with LP and basic first order logic. Appropriate background can be obtained from [168] for LP and [223] for logic. For introductory papers on constraint logic programming and CLP languages we refer the reader to [63, 65, 156, 94] For further reading on CLP we suggest other surveys [58, 109, 110], some collections of papers [20, 143, 111] and some books [107, 214] More generally, papers on CLP appear in various journals and conference proceedings devoted to computational logic, constraint processing or symbolic computation. 7 1.5. Notation and Terminology This paper will (hopefully) ....

P. van Hentenryck, Constraint Satisfaction using Constraint Logic Programming, Artificial Intelligence 58, 113--159, 1992.

....computes over the real numbers. CHIP and Prolog III compute over several domains: Boolean, linear arithmetic over the rational numbers, CHIP over linear arithmetic over finite domains, Prolog III over a domain of strings. The language cc(FD) 40] is basically a second generation CHIP system. In [41] the authors describe how the CLP language cc(FD) can be used to solve the two combinatorial search problems of test pattern generation and car sequencing. Many of the definitions, results, and proofs for the theory of logic programming applies to constraint logic programming as well. The ....

....: vm (r[s] z 1 y 1 ] y 1 = z 2 y 2 ] ym Gamma1 = zm y m] ym = C 1 : Cm ) 2 2 Note that the statement of Theorem 4.2 implies that the formula s = t C is satisfiable. 26 Section 5 Related work Bounded quantifiers in logic programming were considered in [18, 17, 19, 28, 29, 14, 4, 41, 42, 3, 43]. In [18, 19, 17] the concept of Sigma programs have been defined using Sigma formulas. The model theoretic and the fixpoint semantics of our paper are very similar to those of [18, 19, 17] In [28, 29] it is shown how to integrate (flat) finite sets in logic programming with the idea of ....

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P. Van Hentenryck, H. Simonis, and M. Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58:113--159, 1992.

....providing such information are available as commercial products. One system providing this ability is Refine [Burn, 1992] Other researchers have created similar tools as part of ongoing research, and under various kinds of agreements make them available for academic use. One such tool is Genoa [Devanbu, 1992], a language independent code analyzer. With Genoa, Devanbu and Eaves [Devanbu and Eaves, 1994] have constructed Gen , a proprietary tool which generates tools for analysis of C code. Specifically, Gen can generate tools which in turn generate annotated abstract syntax trees (ASTs) of C ....

....been studied extensively, and a variety of problem domains have been formulated in this framework. To list even a representative cross section of these papers would be difficult, however, some recent applications and evaluations include [Tolba et al. 1991] Yang and Fong, 1992] Norvig, 1992] [Van Hentenryck et al. 1992b] Guan and Friedrich, 1992] Nadel, 1989] and [Nadel, 1990] Many authors have been noted for continued interest in broad discussions of the applicability of CSP and specific theoretical and practical contributions, however, the most notable are perhaps Mackworth, Dechter and Freuder (see for ....

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P. Van Hentenryck, H. Simonis, and M. Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58:113-- 159, December 1992.

.... algorithms (Van Hentenryck, Deville and Teng 1992) This has been used in constraint logic programming systems by representing the domain as an interval and evaluating constraints using interval arithmetic, since interval arithmetic only uses the interval bounds to evaluate an expression (Van Hentenryck, Simonis and Dincbas 1992). In the cases where the interval representation of Section 2.1.1 applies and the constraints are monotone, we need only check endpoints (the bounds of the interval) to achieve consistency. Thus, we exploit optimal time complexity algorithms, where arc consistency can be found in linear time with ....

....can be found in linear time with respect to the number of constraints (Darr 1997) 2.2.2. Decomposability Decomposability, or n consistency, is a stronger property than consistency. Decomposability means that any combination of domain values satisfies all the constraints (Freuder 1978; van Beek 1992). The predicate decomposable(c j ) is true if c is decomposable; the predicate decomposable(v i ) is true if decomposable(c j ) for every c j that includes a domain attribute of v i in its arguments. Decomposability is the ultimate goal of any CSP solver. 2.2.3. Monotonicity Monotonicity is a ....

Van Hentenryck, P., H. Simonis and M. Dincbas: 1992, Constraint satisfaction using constraint logic programming. Artificial Intelligence ,58(1-3): 113-159.

....R. Apt and Eric Monfroy j t f u t t f u f f t u u u u u that determines a ternary constraint with nine triples. We obtain for it 20 equality rules and 26 membership rules. Typical examples are equiv(X,Y,f) X##u,Y##u. and equiv(t,X,Y) in(Y, f, u] X##t. Six valued logic In (Van Hentenryck et al. 1992) the constraint logic programming language CHIP is used for the automatic test pattern generation (ATPG) for the digital circuits. To this end the authors define a specific six valued logic and provide some rules (expressed in the form of so called demons) to carry out the constraint propagation. ....

.... Gamma Gamma dnot 0 enot The Equality Rules Generation algorithm generated 41 equality rules in 0.15 seconds, while the Membership Rules Generation algorithm generated 155 membership rules in 14.35 seconds. It is difficult to compare the outcome of these two algorithms with the rules given in (Van Hentenryck et al. 1992)[page 133] because some of the latter ones allow equalities between the variables in the premise. However, it is clear that our approach is more systematic and fully automatic. Propagating signs As a next example consider the rules for propagating signs in arithmetic expressions, see, e.g. ....

Van Hentenryck, P., Simonis, H., & Dincbas, M. (1992). Constraint satisfaction using constraint logic programming. Artificial intelligence, 58, 113--159.

....Y are true then set Z to true (for and(X,Y,Z) Note the difference with the clp(B FD) formulation where the primitive X in r was used in a computational way to calculate the value (0 or 1) to assign. The behavior of this primitive is very similar to the ask definition of and(X,Y,Z) presented in [21]. Thus, we propose a primitive constraint l 0 = l 1 ; l n where c : l = l, l] constraint) l : X (positive literal) X (negative literal) Table 2. Syntax of the constraint l 0 = l 1 ; l n each l i is either a positive literal (X) or a negative literal ( GammaX ) see ....

P. Van Hentenryck, H. Simonis and M. Dincbas. Constraint Satisfaction Using Constraint Logic Programming. Artificial Intelligence no 58, pp 113-159, 1992.

.... for certain classes of SAT problems (GSAT [17] GENET [8] CSAT [10] Other works in constraint programming language design (PROLOG III [7] CHIP [20] ILOG SOLVER [11] propose several language features for describing concisely constraint satisfaction problems on boolean and numerical domains [22], and help users to solve their problems with constraint satisfaction techniques. Certain kinds of SAT problems that we call structured SAT problems, because they can be described in a high level language with small sets of boolean constraints (for example cardinality constraints) are ....

P. Van Hentenryck, H. Simonis, M. Dincbas. Constraint satisfaction using constraint logic programming, Artificial Intelligence 58, p 113159, 1992.

....optimality but cannot in general handle as large problems as the other methods can. However, constraint based search techniques provide means of aggressively pruning the search space, and can make global search a feasible alternative for large problems. The notion of constraint propagation [10, 8] has turned out to be possibly the most interesting aspect of constraint based search. This is the technique of deducing, given a set of constraints, as many logical consequences as can be done efficiently, and thereby updating the set with new information. The inferred information is used for ....

....search. Research on constraint propagation aims in the long perspective to develop strong algorithms for efficiently pruning search spaces. So far, research in the field has been mainly devoted to using basic methods of constraint satisfaction inside constraint logic programming languages [10, 8], but when attacking truly hard problems such methods are insufficient. We consider it an important research issue to extend and improve existing constraint propagating methods, from which many industrial applications can gain efficiency, robustness, and clarity. 1.2 Goals 1.2.1 Theorem proving ....

M. Dincbas, P. Van Hentenryck, and H. Simonis. Constraint Satisfaction using constraint logic programming. In Artificial Intelligence, vol 58, 113-159, 1992.

.... analysis [1] however, it is unusual to incorporate arithmetic expressions in the set constraint language and solver (but see [28] for an important partial exception) Note also that techniques for solving integer constraint systems may be found in the artificial intelligence literature [14, 32, 37, 58]; however, their algorithms typically stress generality for small problems ( hundreds of nodes and constraints [14] over scalability and thus are not directly applicable here. LINT LIKE TOOLS. Several commonly used tools [34, 18, 19] use static analysis and some heuristics to detect common ....

P. Van Hentenryck, H. Simonis, M. Dincbas, "Constraint satisfaction using constraint logic programming," Artificial Intelligence, vol.58, 1992, pp.113--159.

....reasoning over constraints. We will, however, first deal with the three major approaches (other than our own) for disjunctive and hypothetical reasoning over constraints. CHAPTER 1. INTRODUCTION 33 1.2. 1 The cc(FD) Language The cc(FD) 20 programming language was recently introduced in [26, 23, 21] as a rational reconstruction of the CHiP language [17, 1] Although described as a concurrent constraint language, it is closer to the CLP(D) approach in that the store is not maintained strongly K consistent, but rather uses an arc consistency algorithm [25] Thus the store may at times be ....

P. Van Hentenryck, H. Simonis, and M. Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58(1--3), December 1992.

....being integrated in a full CLP language, heuristics can be added in the program itself, as opposed to a closed boolean solver with (a finite set of) built in heuristics. Second, being integrated in a finite domains solver, various extensions such as pseudo booleans [2] or multi valued logics [25] can be integrated straightforwardly. Third, being based on a propagation method, searching for a single solution can be done much more quickly if the computation of all solutions is not needed. The rest of this paper is organized as follows. Section 2 introduces boolean constraints and the ....

....the propagation mechanisms that will be used to solve boolean constraints. We have indeed given the operational semantics of the constraint solver in this way. The most elegant way to implement such a solver would be to use some Ask primitive in a concurrent constraint language, as proposed by [25]. We do not have such a facility in clp(FD) and we will encode this propagation scheme by X in r constraints, as is detailed below. 4.3 Correctness and completeness of (B ; B ) It is important to ensure that our (operationally defined) constraint system is equivalent to traditional boolean ....

P. Van Hentenryck, H. Simonis and M. Dincbas. Constraint Satisfaction Using Constraint Logic Programming. Artificial Intelligence no 58, pp 113-159, 1992.

....definition of a good heuristic function that can be computed sufficiently fast in Functional Strips is a subtle problem and there are many possibilities. We think it s an interesting problem on its own. Since both constraints and costs are involved, techniques from constraint programming (e.g. [HSD92]) may turn out to be relevant. 7 Discussion Effective planning requires both good modeling languages and good algorithms. The Strips language has shaped planning since the early 70 s since it provides a compact representation of actions and supports divide and conquer algorithms. In recent ....

....as well. This will be possible only by a suitable combination of general and effective languages and algorithms. We find that the work in Constraint Logic Programming has similar goals, even if it s focused on a different type of decision tasks (CSPs) where it has achieved great success [HSD92]. Some of the refinements and extensions that we would like to explore in the future are the following: ffl Constraints. Constraints represented as formulas can be used to provide implicit preconditions (e.g. GKL97] Namely, the set A(s) of actions applicable in s will exclude all actions a ....

P. Van Hentenryck, H. Simonis, and M. Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58(1--3):113--159, 1992.

.... paradigm is based on the notion of a variable in the mathematical sense (usually called in this context a logical variable) This greatly facilitates the addition of constraints and partly explains why the integration of constraints into logic programming such as in the case of CHIP (see [19]) Prolog III (see [4] and CLP(R) see [11] to name just three examples, has been so smooth and elegant. Further, logic programming languages provide support for automatic backtracking. However, as already mentioned, in constraint logic programming languages types are not available. Moreover, ....

P. Van Hentenryck, Helmut Simonis, and Mehmet Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58:113--159, 1992.

.... great deal of backtracking, unlike the performance found in [4] Given the discussion in section 1, it is natural to try the smallest domain first variable ordering heuristic on any CSP, and this is recommended for the car sequencing problem in a later paper by van Hentenryck, Simonis and Dincbas [13]. In fact, it may not obvious why this heuristic would not choose the variables consecutively, since if the first variable is assigned a value first, the capacity constraints will reduce the domains only of the next few variables, depending on the options required by the selected car. It might be ....

....will show that the 4th variable must also be assigned a car with this option; this variable will thus have the smallest domain. So the 4th variable will be assigned next, then the 7th and so on. In experiments, the fail first heuristic gave poor results, despite the experience reported in [13]. Intuitively, leaving gaps, in the fashion just described, seems likely to cause difficulties in completing the sequence. The cars to be fitted into the gaps have to be compatible with the cars already placed before and after them, which is less likely to be possible than if car has only to be ....

P. van Hentenryck, H. Simonis, and M. Dincbas. Constraint Satisfaction using Constraint Logic Programming. Artificial Intelligence, 58:113--159, 1992.

.... Truth Maintenance [4] Integer Programming [5] Automata Theory [6] Graph Theory [7] Hill Climbing [8] Neural Networks [9] Genetic Algorithms [10] Relational Algebra [11] Constraint Synthesis [12] Disjunctive Decomposition [13] Conjunctive Decomposition [14] Constraint Logic Programming [15], and GSAT [16] We can classify these techniques into (1) problem reduction, 2) solution synthesis, and (3) searching. In problem reduction, we first identify redundant information and then remove them. On the contrary to problem reduction, we generate legal compound labels in solution synthesis ....

H. S. V. Hentenryck and M. Dinebas, "Constraint satisfaction using constraint logic programming," Artificial Intelligence, vol. 58, pp. 113--160, 1992.

....ankte Klasse von logischen Formeln ausgedr uckt. Durch ihre abstrakte deklarative Natur eignen sich LP Sprachen gut f ur die schnelle Erst und Weiterentwicklung von Prototypen auf der Basis unvollst andiger Spezifikationen (Rapid Prototyping) Die Idee der Constraintlogikprogrammierung (CLP) [15, 11, 4] ist, da gewisse logische Pr adikate als Constraints deklarativ und effizient durch spezielle Algorithmen behandelt werden k onnen. Das hei t, da die allgemeine Methode der LP Sprachen, die die Tiefensuche mit chronologischem R ucksetzen (engl. backtracking) verwendet, um spezielle, ....

P. van Hentenryck, H. Simonis, and M. Dincbas. Constraint satisfaction using constraint logic programming. Artificial Intelligence, 58(1-3):113--159, 1992.

....S2 4 ] 2) automatically assigns S2 to 1 and S1 to 5 without any backtracking. More sophisticated handlings of disjunctions, taking for instance several tasks simultaneously, are possible in cc(FD) using, for instance, the cardinality combinator in conjunction with the implication combinator [27]. Note also that, in the perfect square problem, the above handling of disjunctions is generalized to 2 dimensions. Example 8 The cardinality combinator also enables to link Boolean variables (i.e. 0 1 domain variables) with a constraint in the following way: B 2 0. 1, #( B, C] B ) The above ....

....constraints are generated to speed up the computation by pruning the search space early. 3.2.1 Problem Data The program is generic and receives as data the size of the master square and the sizes of the squares. For instance the data for 21 squares is as follows: sizeMaster(112) sizeSquares([50,42,37,35,33,29,27,25,24,19,18,17,16,15,11,9,8,7,6,4,2]) 3.2.2 Program Variables Each square i is associated with two variables X i and Y i representing the coordinates of the bottom left corner of the square. Each of these variables ranges between 1 and S Gamma S i 1 where S is the size of the master square and S i is the size of square i. The ....

P. Van Hentenryck, H. Simonis, and M. Dincbas. Constraint Satisfaction Using Constraint Logic Programming. Artificial Intelligence, 1992. (Special Issue on ConstraintBased Reasoning), accepted for publication. 26

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Van Hentenryk, P.; Simonis, H.; and Dincbas, M. 1992b. Constraint satisfaction using constraint logic programming. Artificial Intelligence 58:113--159.

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Van Hentenryck, P., Simonis, H. and Dincbas, D. Constraint satisfaction using constraint logic programming, Artiřcial Intelligence, vol 58, no.1-3, p113-157, December 1992.

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P. Van Hentenryck, H. Simonis and M. Dincbas (1992) Constraint satisfaction using constraint logic programmging AI 58.

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