A. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction. John Wiley and Sons, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Delta T Delta x in ; 2 Delta x in d 1 ; x in d 2 2 Delta x in d 1 d 2 Table 2.8: Evaluating domain constraints 2. 5 Related and Future Work Our proof system goes beyond resolution and Davis Putnam like procedures [Rob65, DP60] by combining propagation of arithmetic constraints [Mac88, DHS 88] with the propagation of propositional constraints. Dilemma lets us use speculative work constructively by asserting formulas shared between disjunctive branches, somewhat like the splitting rule of Davis Putnam [DP60, US94] Boolean formulas over linear constraints have been ....

A. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction. John Wiley and Sons, 1988.

.... Delta T Delta x in ; 2 Delta x in d 1 ; x in d 2 2 Delta x in d 1 d 2 Table 2.8: Evaluating domain constraints 2. 5 Related and Future Work Our proof system goes beyond resolution and Davis Putnam like procedures [Rob65, DP60] by combining propagation of arithmetic constraints [Mac88, DHS 88] with the propagation of propositional constraints. Dilemma lets us use speculative work constructively by asserting formulas shared between disjunctive branches, somewhat like the splitting rule of Davis Putnam [DP60, US94] Boolean formulas over linear constraints have been ....

A. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction. John Wiley and Sons, 1988.

....In this way, we make the SCSP framework more flexible, since it can be used also when it is difficult to assign values to tuples and instead it is easier to rate some of the solutions. Learning Solution Preferences in CSPs 3 1 Introduction Classical constraint satisfaction problems (CSPs) [Mon74, Mac88] are a very expressive and natural formalism to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such ....

....concepts of learning via gradient descent, and Section 4 describes our approach. Finally Section 5 considers the universality problem, and Section 6 discusses the significance of the proposed approach. 2 Standard and Non Standard Constraint Systems Standard constraint satisfaction problems (CSPs) [Mon74, Mac88] consist of a set of variables with a finite domain, plus a set of constraints. Each constraint involves a subset of the variables and specifies the tuples of values allowed for those variables. A solution for a CSP is then an assignment of values to all the variables such that all constraints are ....

A.K. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....requirements checked, and the corresponding context free productions combined to get the resulting context sensitive rule. Of course, all these tasks are to be performed in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [Mac88, Mon74], and the propagation and solution techniques associated to them [Mac88, Mon74, Mac77, Fre78, MF85, DP88] may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a ....

....to get the resulting context sensitive rule. Of course, all these tasks are to be performed in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [Mac88, Mon74] and the propagation and solution techniques associated to them [Mac88, Mon74, Mac77, Fre78, MF85, DP88], may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset of the variables and specifies all the possible ways such variables can satify the constraint. ....

[Article contains additional citation context not shown here]

A.K. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....preferences coincide with the examples. In this way, we make the SCSP framework more flexible, since it can be used also when it is difficult to assign values to tuples and instead it is easier to rate some of the solutions. 1 Introduction Classical constraint satisfaction problems (CSPs) [Mon74, Mac88] are a very expressive and natural formalism to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such ....

....the basic concepts of learning via gradient descent, and Section 4 describes our approach. Finally Section 5 considers the universality problem, and Section 6 discusses the significance of the proposed approach. 2 Standard and Non Standard Constraint Systems Standard constraint problems (CSPs) [Mon74, Mac88] consist of a set of variables with a finite domain, plus a set of constraints. Each constraint involves a subset of the variables and specifies the tuples of values allowed for those variables. A solution for a CSP is then an assignment of values to all the variables such that all constraints are ....

A.K. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....on the synchronization requirements over the shared variables. The construction of these rewriting steps from the simple context free productions in practice can be a very costly combinatorial problem (called the rulematching problem in [2] In this respect, finite domain constraint problems [7, 9], and the propagation and solution techniques associated to them [8] may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset of the variables and ....

....synchronization requirements posed by the synchronized productions. In other words, the sequents of the tile logic correspond exactly to those derivations which are allowed in the given synchronized graph rewriting system 1 . CONSTRAINT PROPAGATION A (finite domain) constraint problem (CSP) [7, 9] consists of a set of variables ranging over a finite domain, and a set of constraints. A solution to such problem is an instantiation of all the variables such that all the constraints are satisfied. Formally, a CSP is a tuple hV; D;C; con; defi, where V is a finite set of variables (i.e. V = ....

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A.K. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....totally ordered commutative monoid. While comparing the two approaches, we show how to pass from one to the other one, and we discuss when this is possible. The two frameworks have been independently introduced in [2, 3] and [34] 1. Introduction Classical constraint satisfaction problems (CSPs) [24, 26] are a very expressive and natural formalism to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such ....

....interpreted as cost, or degrees of preference, or probabilities, or others) and the two operations define a way to combine constraints together. Specific choices of the semiring will then give rise to different instances of the framework. In classical CSPs, so called local consistency techniques [11, 12, 23, 24, 26, 27] have been proved to be very effective when approximating the solution of a problem. In this paper we study how to generalize this notion to this framework, and we provide some sufficient conditions over the semiring operations which guarantee that such algorithms can also be fruitfully applied to ....

[Article contains additional citation context not shown here]

A. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....requirements checked, and the corresponding context free productions combined to get the resulting context sensitive rule. Of course, all these tasks are to be performed in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [26, 29], and the propagation and solution techniques associated to them [26, 29, 25, 11, 27, 8] may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset of the ....

....to get the resulting context sensitive rule. Of course, all these tasks are to be performed in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [26, 29] and the propagation and solution techniques associated to them [26, 29, 25, 11, 27, 8], may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset of the variables and specifies all the possible ways such variables can satisfy the constraint. ....

[Article contains additional citation context not shown here]

A.K. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....requirements checked, and the corresponding context free productions combined to get the resulting context sensitive rule. Of course, all these tasks are to be performed in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [30, 35], and the propagation and solution techniques associated to them [30, 35, 29, 19, 31, 12] may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset of the ....

....to get the resulting context sensitive rule. Of course, all these tasks are to be performed in a distributed way, since we assumed to be in a distributed environment. In this respect, finite domain constraint problems [30, 35] and the propagation and solution techniques associated to them [30, 35, 29, 19, 31, 12], may be helpful. A finite domain constraint problem can be described as a set of variables taking values over corresponding finite domains, and a set of constraints. Each constraint involves a subset of the variables and specifies all the possible ways such variables can satisfy the constraint. A ....

[Article contains additional citation context not shown here]

A.K. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....solving schemes, thus allowing one both to formally justify many informally taken choices in existing schemes, and to prove that the local consistency techniques can be used also in newly defined schemes. 1 Introduction Classical constraint satisfaction problems (CSPs) Montanari, 1974; Mackworth, 1988 ] are a very expressive and natural formalism to specify many kinds of reallife problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such ....

....of preference, or probabilities, or others) and the two operations define a way to combine constraints together. Specific choices of the semiring will then give rise to different instances of our framework. In classical CSPs, the so called local consistency techniques [ Freuder, 1978; 1988; Mackworth, 1988; 1977; Montanari, 1974; Montanari and Rossi, 1991 ] have been proved to be very effective when approximating the solution of a problem. In this paper we study how to generalize this notion to our framework, and we provide some sufficient conditions over the semiring operations which guarantee ....

[Article contains additional citation context not shown here]

A.K. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. We then compare the two approaches and we discuss the relationship between them. 1 Introduction Classical constraint satisfaction problems (CSPs) [19, 17] are a very expressive and natural formalism to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such ....

....as cost, or degrees of preference, or probabilities, or others) and the two operations define a way to combine constraints together. Specific choices of the semiring will then give rise to different instances of the framework. In classical CSPs, the so called local consistency techniques [8, 9, 17, 16, 19, 20] have been proved to be very effective when approximating the solution of a problem. In this paper we study how to generalize this notion to this framework, and we provide some sufficient conditions over the semiring operations which guarantee that such algorithms can be fruitfully applied also to ....

[Article contains additional citation context not shown here]

A.K. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

....based on a semiring, and the other one on a totally ordered commutative monoid. We then compare the two approaches and we discuss the relationship between them. The two frameworks have been independently introduced in [2] and [28] 1 Introduction Classical constraint satisfaction problems (CSPs) [18, 20] are a very expressive and natural formalism to specify many kinds of real life problems. In fact, problems ranging from map coloring, vision, robotics, job shop scheduling, VLSI design, etc. can easily be cast as CSPs and solved using one of the many techniques that have been developed for such ....

....interpreted as cost, or degrees of preference, or probabilities, or others) and the two operations define a way to combine constraints together. Specific choices of the semiring will then give rise to different instances of the framework. In classical CSPs, so called local consistency techniques [9, 10, 17, 18, 20, 21] have been proved to be very effective when approximating the solution of a problem. In this paper we study how to generalize this notion to this framework, and we provide some sufficient conditions over the semiring operations which guarantee that such algorithms can also be fruitfully applied to ....

[Article contains additional citation context not shown here]

A. Mackworth. Encyclopedia of AI, chapter Constraint Satisfaction, pages 205--211. Springer Verlag, 1988.

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