Constraint Processing

2011 ◽  
pp. 404-409
Author(s):  
Roman Barták
Keyword(s):  
Logic Programming ◽  
Constraint Satisfaction ◽  
Optimization Problems ◽  
Constraint Satisfaction Problem ◽  
Constraint Logic Programming ◽  
Constraint Satisfaction Problems ◽  
Start Time ◽  
Constraint Processing ◽  
Available Technology ◽  
3D Scene

Constraints appear in many areas of human endeavour starting from puzzles like crosswords (the words can only overlap at the same letter) and recently popular Sudoku (no number appears twice in a row) through everyday problems such as planning a meeting (the meeting room must accommodate all participants) till solving hard optimization problems for example in manufacturing scheduling (a job must finish before another job). Though all these problems look like being from completely different worlds, they all share a similar base – the task is to find values of decision variables, such as the start time of the job or the position of the number at a board, respecting given constraints. This problem is called a Constraint Satisfaction Problem (CSP). Constraint processing emerged from AI research in 1970s (Montanary, 1974) when problems such as scene labelling were studied (Waltz, 1975). The goal of scene labelling was to recognize a type of line (and then a type of object) in the 2D picture of a 3D scene. The possible types were convex, concave, and occluding lines and the combination of types was restricted at junctions of lines to be physically feasible. This scene labelling problem is probably the first problem formalised as a CSP and some techniques developed for solving this problem, namely arc consistency, are still in the core of constraint processing. Systematic use of constraints in programming systems has started in 1980s when researchers identified a similarity between unification in logic programming and constraint satisfaction (Gallaire, 1985) (Jaffar & Lassez, 1987). Constraint Logic Programming was born. Today Constraint Programming is a separate subject independent of the underlying programming language, though constraint logic programming still plays a prominent role thanks to natural integration of constraints into a logic programming framework. This article presents mainstream techniques for solving constraint satisfaction problems. These techniques stay behind the existing constraint solvers and their understanding is important to exploit fully the available technology.

scholarly journals A Variable Depth Search Algorithm for Binary Constraint Satisfaction Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
N. Bouhmala
Keyword(s):  
Constraint Satisfaction ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Wide Spectrum ◽  
Constraint Satisfaction Problem ◽  
Practical Interest ◽  
Constraint Satisfaction Problems ◽  
Variable Depth ◽  
The Past ◽  
Binary Constraint

The constraint satisfaction problem (CSP) is a popular used paradigm to model a wide spectrum of optimization problems in artificial intelligence. This paper presents a fast metaheuristic for solving binary constraint satisfaction problems. The method can be classified as a variable depth search metaheuristic combining a greedy local search using a self-adaptive weighting strategy on the constraint weights. Several metaheuristics have been developed in the past using various penalty weight mechanisms on the constraints. What distinguishes the proposed metaheuristic from those developed in the past is the update ofkvariables during each iteration when moving from one assignment of values to another. The benchmark is based on hard random constraint satisfaction problems enjoying several features that make them of a great theoretical and practical interest. The results show that the proposed metaheuristic is capable of solving hard unsolved problems that still remain a challenge for both complete and incomplete methods. In addition, the proposed metaheuristic is remarkably faster than all existing solvers when tested on previously solved instances. Finally, its distinctive feature contrary to other metaheuristics is the absence of parameter tuning making it highly suitable in practical scenarios.

scholarly journals Models and Tools for Improving Efficiency in Constraint Logic Programming

2011 ◽  
Vol 5 (1) ◽  
pp. 69-78 ◽  
Author(s):  
Antoni Ligęza
Keyword(s):  
Logic Programming ◽  
Constraint Satisfaction ◽  
Constraint Logic Programming ◽  
Constraint Satisfaction Problems ◽  
Combinatorial Explosion ◽  
Entropy Minimization ◽  
Hypergraph Model ◽  
Planning Approach ◽  
Strategy Planning

Constraint Satisfaction Problems typically exhibit strong combinatorial explosion. In this paper we present some models and techniques aimed at improving efficiency in Constraint Logic Programming. A hypergraph model of constraints is presented and an outline of strategy planning approach focused on entropy minimization is put forward. An example cryptoaritmetic problem is explored in order to explain the proposed approach.

scholarly journals Statistical physics of hard optimization problems

2009 ◽  
Vol 59 (3) ◽  
Author(s):  
Lenka Zdeborová
Keyword(s):  
Cost Function ◽  
Constraint Satisfaction ◽  
Disordered Systems ◽  
Statistical Physics ◽  
Optimization Problems ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Cavity Method ◽  
Complete Class ◽  
Np Complete

Statistical physics of hard optimization problemsOptimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a cost function depending on these variables. Optimization problems in the non-deterministic polynomial (NP)-complete class are particularly difficult, it is believed that the number of operations required to minimize the cost function is in the most difficult cases exponential in the system size. However, even in an NP-complete problem the practically arising instances might, in fact, be easy to solve. The principal question we address in this article is: How to recognize if an NP-complete constraint satisfaction problem is typically hard and what are the main reasons for this? We adopt approaches from the statistical physics of disordered systems, in particular the cavity method developed originally to describe glassy systems. We describe new properties of the space of solutions in two of the most studied constraint satisfaction problems - random satisfiability and random graph coloring. We suggest a relation between the existence of the so-called frozen variables and the algorithmic hardness of a problem. Based on these insights, we introduce a new class of problems which we named "locked" constraint satisfaction, where the statistical description is easily solvable, but from the algorithmic point of view they are even more challenging than the canonical satisfiability.

Design Approaches for Wire Robots

2009 ◽  
Author(s):  
Tobias Bruckmann ◽  
Lars Mikelsons ◽  
Thorsten Brandt ◽  
Manfred Hiller ◽  
Dieter Schramm
Keyword(s):  
Constraint Satisfaction ◽  
Optimization Problems ◽  
Constraint Satisfaction Problem ◽  
Specific Task ◽  
Analysis Problem ◽  
End Effector ◽  
Practical Applications ◽  
Workspace Analysis ◽  
Discrete Methods ◽  
Reliability And Robustness

Wire robots consist of a movable end-effector which is connected to the machine frame by motor driven wires. Since wires can transmit only tension, positive wire forces have to be ensured. During workspace analysis, the wires forces need to be calculated. Discrete methods do not produce satisfying results, since intermediate points on the discrete calculation grids are neglected. Using intervals instead of points leads to reliable results. Formulating the analysis problem as a Constraint-Satisfaction-Problem (CSP) allows convenient transition to the synthesis problem, i.e. to find suitable designs for practical applications. In this paper, two synthesis approaches are employed: Design-to-Workspace (i.e. calculation of an optimal robot layout for a given workspace) and an extension called Design-to-Task (i.e. calculation of the optimal robot for a specific task). To solve these optimization problems, the paper presents approaches to combine the reliability and robustness of interval-based computations with the effectiveness of available optimizer implementations.

scholarly journals Constraint Satisfaction Problems and Their Reduction to Directed Graphs

2021 ◽  
Author(s):  
Muhanda Stella Mbaka Muzalal
Keyword(s):  
Constraint Satisfaction ◽  
Cell Phone ◽  
Constraint Satisfaction Problem ◽  
Directed Graphs ◽  
Oriented Graph ◽  
Constraint Satisfaction Problems ◽  
Systems Of Equations ◽  
Relational Structures ◽  
Algorithmic Problems ◽  
Boolean Formulas

Constraint satisfaction problems present a general framework for studying a large class of algorithmic problems such as satisfaction of Boolean formulas, solving systems of equations over finite fields, graph colourings, as well as various applied problems in artificial intelligence (scheduling, allocation of cell phone frequencies, among others.) CSP (Constraint Satisfaction Problems) bring together graph theory, complexity theory and universal algebra. It is a well known result, due to Feder and Vardi, that any constraint satisfaction problem over a finite relational structure can be reduced to the homomorphism problem for a finite oriented graph. Until recently, it was not known whether this reduction preserves the type of the algorithm which solves the original constraint satisfaction problem, so that the same algorithm solves the corresponding digraph homomorphism problem. We look at how a recent construction due to Bulin, Deli´c, Jackson, and Niven can be used to show that the polynomial solvability of a constraint satisfaction problem using Datalog, a programming language which is a weaker version of Prolog, translates from arbitrary relational structures to digraphs.

Equations in oligomorphic clones and the constraint satisfaction problem for ω-categorical structures

2019 ◽  
Vol 19 (02) ◽  
pp. 1950010 ◽  
Author(s):  
Libor Barto ◽  
Michael Kompatscher ◽  
Miroslav Olšák ◽  
Van Pham Trung ◽  
Michael Pinsker
Keyword(s):  
Constraint Satisfaction ◽  
Short Proof ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Ramsey Property ◽  
Categorical Structure ◽  
Homogeneous Structures ◽  
Identity Modulo ◽  
Rational Order ◽  
Its Polymorphism

There exist two conjectures for constraint satisfaction problems (CSPs) of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain nontrivial linear identity modulo outer embeddings. The second conjecture, challenging the approach via model-complete cores by reflections, states that tractability is equivalent to the linear identities (without outer embeddings) satisfied by its polymorphisms clone, together with the natural uniformity on it, being nontrivial. We prove that the identities satisfied in the polymorphism clone of a structure allow for conclusions about the orbit growth of its automorphism group, and apply this to show that the two conjectures are equivalent. We contrast this with a counterexample showing that [Formula: see text]-categoricity alone is insufficient to imply the equivalence of the two conditions above in a model-complete core. Taking another approach, we then show how the Ramsey property of a homogeneous structure can be utilized for obtaining a similar equivalence under different conditions. We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a nontrivial system of linear identities, and obtain nontrivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset. Finally, we provide a new and short proof, in the language of monoids, of the theorem stating that every [Formula: see text]-categorical structure is homomorphically equivalent to a model-complete core.

Symbolic Solutions for Symbolic Constraint Satisfaction Problems

2020 ◽  
Author(s):  
Alexsander Andrade de Melo ◽  
Mateus De Oliveira Oliveira
Keyword(s):  
Constraint Satisfaction ◽  
Existence Of Solutions ◽  
Constraint Satisfaction Problem ◽  
Constant Width ◽  
Computable Function ◽  
Constraint Satisfaction Problems ◽  
Decision Diagrams ◽  
Turing Machines ◽  
Branching Programs ◽  
Hard Problems

A fundamental drawback that arises when one is faced with the task of deterministically certifying solutions to computational problems in PSPACE is the fact that witnesses may have superpolynomial size, assuming that NP is not equal to PSPACE. Therefore, the complexity of such a deterministic verifier may already be super-polynomially lower-bounded by the size of a witness. In this work, we introduce a new symbolic framework to address this drawback. More precisely, we introduce a PSPACE-hard notion of symbolic constraint satisfaction problem where both instances and solutions for these instances are implicitly represented by ordered decision diagrams (i.e. read-once, oblivious, branching programs). Our main result states that given an ordered decision diagram D of length k and width w specifying a CSP instance, one can determine in time f(w,w')*k whether there is an ODD of width at most w' encoding a solution for this instance. Intuitively, while the parameter w quantifies the complexity of the instance, the parameter w' quantifies the complexity of a prospective solution. We show that CSPs of constant width can be used to formalize natural PSPACE hard problems, such as reachability of configurations for Turing machines working in nondeterministic linear space. For such problems, our main result immediately yields an algorithm that determines the existence of solutions of width w in time g(w)*n, where g:N->N is a suitable computable function, and n is the size of the input.

PREPROCESSING QUANTIFIED CONSTRAINT SATISFACTION PROBLEMS WITH VALUE REORDERING AND DIRECTIONAL ARC AND PATH CONSISTENCY

2008 ◽  
Vol 17 (02) ◽  
pp. 321-337 ◽  
Author(s):  
KOSTAS STERGIOU
Keyword(s):  
Constraint Satisfaction ◽  
Early Stage ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Combinatorial Problems ◽  
Arc Consistency ◽  
Solution Methods ◽  
Speed Up ◽  
Phase Transition Region ◽  
The Impact

The Quantified Constraint Satisfaction Problem (QCSP) is an extension of the CSP that can be used to model combinatorial problems containing contingency or uncertainty. It allows for universally quantified variables that can model uncertain actions and events, such as the unknown weather for a future party, or an opponent's next move in a game. Although interest in QCSPs is increasing in recent years, the development of techniques for handling QCSPs is still at an early stage. For example, although it is well known that local consistencies are of primary importance in CSPs, only arc consistency has been extended to quantified problems. In this paper we contribute towards the development of solution methods for QCSPs in two ways. First, by extending directional arc and path consistency, two popular local consistencies in constraint satisfaction, to the quantified case and proposing an algorithm that achieves these consistencies. Second, by showing how value ordering heuristics can be utilized to speed up computation in QCSPs. We study the impact of preprocessing QCSPs with value reordering and directional quantified arc and path consistency by running experiments on randomly generated problems. Results show that our preprocessing methods can significantly speed up the QCSP solving process, especially on hard instances from the phase transition region.

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