J. de Kleer. A comparison of ATMS and CSP techniques. In Proc. of the 11th IJCAI. International Joint Conference on Artificial Intelligence, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....unit propagation. We re prove this result and extend it to arcinconsistency. Bennaceur also proved that a CSP is arc consistent iff its literal encoding has no unit clauses, and strong path consistent iff it has no unit or binary clauses. The direct encoding of a CSP into a SAT problem appears in [dK89]. G enisson and J egou proved that, with suitable branching heuristics, DP is equivalent to FC applied to the direct encoding [GJ96] Apt has also looked at propagation rules for Boolean constraints [A99] He proves an equivalence between Boolean constraint propagation and unit propagation, and ....

J. de Kleer. A comparison of ATMS and CSP techniques. In Proc. of the 11th IJCAI. International Joint Conference on Artificial Intelligence, 1989.

....other work in this eld. The ltering algorithm presented in [18] achieves arc consistency by communicating the domains of each process to the neighbors and removing values from these domains that cannot satisfy the given constraints. The hyper resolutionbased consistency algorithm reported in [3] applies a logical transformation rule to combine communicated constraints and information on an agent s domain to form tighter constraints. Both algorithms do not transmit abstract constraint information but concrete domains or no good sets of variable labelings that are inconsistent. Hence, one ....

J. de Kleer. A comparison of ATMS and CSP techniques. In Proceedings of the Eleventh International Joint Conference on Articial Intelligence (IJCAI-89), pages 290-296, 1989.

....consistency testing. Because of the potential for generating an exponential number of additional derived constraints, dependency directed backtracking is a particularly expensive form of backjumping. The ATMS universal propagation algorithm can also be applied to the Boolean translation of a CSP [ de Kleer, 1989 ] In addition to clauses generated by the translation, one can specify each assumption of the form X = x as a possible premise. An additional proposition called all variables assigned can be introduced such that BCP can derive the proposition allvariables assigned if and only if a ....

de Kleer, J., A comparison of ATMS and CSP techniques, Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, Detroit, MI (August 1989).

....game is presented in [DG84] If all the atoms that appear in the theory are known a priori (say, in a list provided as part of the input) then the algorithm terminates in time O(n) where n is the total number of occurrences of literals in the theory. The following inference rule, adapted from [de 89] provides a deductive system for the facts that are inferred from a theory using Horn Pebbling: p) p; ff 1 ; ff n ) ff 1 ; ff n ) Delta Delta Delta Delta Delta Delta Delta Delta Delta DHP 27 fi(f ....

....This rule is merely modus ponens with one antecedent restricted to an atom and the other to a clause (recall that (p) is a clausal representation of the atom p) An atom p in a theory Gamma is pebbled iff either (p) or f is inferable from Gamma using the above inference rule. As observed by [de 89] the second antecedent clause, which is a superclause of the consequence clause in the inference rule, may be removed from the theory after this rule is applied, since its further use can be replaced by the consequence clause. The rewrite system, HP, of Figure 2.5 provides an alternative ....

[Article contains additional citation context not shown here]

J. de Kleer. A comparison of ATMS and CSP techniques. In Proceedings Eleventh International Joint Conference on Artificial Intelligence (IJCAI-89), pages 290--296, 1989.

....average) for graph colouring algorithms like the Brelaz heuristic [29] Each test set contains 100 instances except for the 50 vertex test set, which comprises 1,000 instances. The GCP instances were transformed into SAT by using a straightforward, yet efficient encoding known from the literature [12] (see also Appendix A) 4.3. PLANNING INSTANCES Recently it has been shown that some AI Planning problems can be efficiently solved by encoding them into SAT and then finding models of the SAT formulae using standard SAT algorithms like the SLS algorithms applied in our study. sat2000.tex; ....

J. de Kleer. A Comparison of ATMS and CSP Techniques. In Proceedings of IJCAI'89, pages 290--296. Morgan Kaufmann Publishers, 1989.

....N = O(ab 2 cde cd) O(ab 2 cde) and L = O(ab 2 cde) as well. Although these bounds are higher than the bounds for the original CSP, they are not substantially higher. There seems to be only one other algorithm in the literature, due to deKleer, for converting CSP s to SAT problems [dK89] DeKleer s algorithm encodes the CSP variables exactly the same way, but it encodes each CSP constraint by constructing a clause of length O(e) for every possible tuple which does not appear in that constraint. There can be O(b e ) such tuples, so for this algorithm P = O(ab) N = O(ab 2 ....

....If we represent them in some sort of algebraic constraint language, however, then CSP s can be far more expressive. More specifically, both SAT problems and CSP s with tuples have two main disadvantages: they are not good for encoding constraints whose variables range over very large domains [dK89] and they are not good for encoding constraints that involve arithmetic, although Stamm Wilbrandt has created a SAT encoding for addition that ameliorates this latter problem somewhat; for example, his encoding makes it possible to encode an instance of the vertex covering problem [GJ79] using ....

Johan de Kleer. A comparison of ATMS and CSP techniques. In Proceedings of IJCAI-89, pages 290--296, August 1989.

....revision or on finding what holds under all minimal revisions. Here we focus on the identification of a minimum number of changes to represent minimal change. When originally introduced, algorithms for Truth Maintenance were not accompanied by complexity analysis, or performance guarantees [13, 6, 20]. Nevertheless, experimental work with these tools, and more recent complexity analysis, have shown that both JTMS and ATMS functionalities are very inefficient, with ATMS exhibiting higher complexity than JTMS in both time and space. A common strategy for reducing computational complexity has ....

....the language of constraints has the same expressive power as propositional logic [20] all the algorithms presented here are applicable to propositional languages. The connection between truth maintenance systems and constraint satisfaction problems was already pointed out by several authors e.g. [6] and [23] 21] The main thrust of these efforts has been to show that search reduction techniques developed in one area may be used to the benefit of the other. Our work here take this idea one step further. We present the algorithms in a distributed fashion, that is, assigning a processor to ....

[Article contains additional citation context not shown here]

J. de Kleer. A comparison of ATMS and CSP techniques. In Proceedings of IJCAI-89, pages 290--296, Detroit, Michigan, 1989.

....average) for graph colouring algorithms like the Brelaz heuristic [9] Each test set contains 100 instances except for the 50 vertex test set, which comprises 1,000 instances. The GCP instances were transformed into SAT by using a straightforward, yet efficient encoding known from the literature [4]. The characteristic of the SATLIB test sets thus obtained are shown in Table II. Table II. SAT encoded Graph Colouring test sets (flat random graphs) test set instances vertices edges colours vars clauses flat50 115 1,000 50 115 3 150 545 flat75 180 100 75 180 3 225 840 flat100 239 100 100 ....

....sw100 8 lpx c5, where x 2 f0;1; g indicates a morphing ratio of 2 x . Each of these test sets contains 100 instances which were generated using a generator program provided by Toby Walsh and then encoded into SAT using the same encoding as the graph colouring instances described above [4]. The underlying graphs have 100 vertices and 400 edges, the regular ring lattice used for morphing connects each vertex to its 8 nearest neighbours in the cyclic ordering. For 0 p 1, the chromatic number of the graphs thus obtained varies. Using a special graph colouring program provided by ....

J. de Kleer. A Comparison of ATMS and CSP Techniques. In Proceedings of IJCAI'89, pages 290--296. Morgan Kaufmann Publishers, 1989.

....Truth Maintenance Systems (ATMSs) an implementation approach we experimented with our C prototype. However, the overhead of maintaining information about performed inferences is too high compared with the time saved in the propagation phase (for a comparison between ATMS and CSP techniques, see [3]) The integration of reasoning and retrieving mechanisms for problem solving is however an important area for future investigation. 8 Conclusions From the modeling point of view, the layered approach proves to be essential even on simple case studies, in order to develop a model with limited ....

J. de Kleer. A comparison of ATMS and CSP techniques. Int. Joint Conference on Artificial Intelligence, 1989.

....is to apply some natural transformation from CSP to SAT to any CSP , obtaining a CNF formula OE( and identify the resolution refutations of OE( with the resolution refutations of . This was done, for the limited purposed of examining the logical properties of local consistency processing, in [6]. In [9] this approach was used to show the simulation of common CSP algorithms by resolution, and we adopt it also. For a CSP instance = hV; D;Ci, we define the standard encoding of , denoted OE( to be the CNF formula defined as follows. For each CSP variable v 2 V , we have jDj ....

Johann De Kleer, `A comparison of ATMS and CSP techniques ', in Proc. IJCAI 89, pp. 290--296, (1989).

....(ATMSs) an implementation approach we experimented with our C prototype. However, the overhead of maintaining information about performed inferences (i.e. domain reductions) is too high compared with the time saved in the propagation phase (for a comparison between ATMS and CSP techniques, see [4]) The integration of reasoning and retrieving mechanisms for problem solving is however an important area for future investigation. 8 Conclusions From the modeling point of view, the layered approach proves to be essential, even on simple case studies, in order to develop a model with limited ....

J. de Kleer. A comparison of ATMS and CSP techniques. Int. Joint Conference on Articial Intelligence, 1989.

....Bin Packing, or Hamilton Circuit, can be quite naturally formulated as discrete constraint satisfaction problems. When encoding such CSP formulations into SAT, perhaps the most intuitive way is to encode each assignment of a value to a CSP variable by a different propositional variable [de Kleer, 1989] . We call this the sparse encoding, since it results in relatively sparse constraint graphs 3 for the resulting CNF formulae. This encoding strategy requires jDj n variables, where jDj is the domain size and n the number of CSP variables. 4 Given the intuition that high solution densities ....

J. de Kleer. A Comparison of ATMS and CSP Techniques. In Proc. IJCAI'89. Morgan Kaufmann, 1989.

....procedures have influenced much other work in this field. The same holds for the coordination protocols in this article. Also in [25] two constraint propagation techniques are mentioned: a filtering algorithm reported in [22] and a hyper resolution based consistency algorithm described in [2]. The filtering algorithm achieves arcconsistency by communicating the domains of each process to the neighbors and removing values from these domains that cannot satisfy the given constraints. The hyper resolution based consistency algorithm applies a logical transformation rule to combine ....

J. de Kleer. A comparison of ATMS and CSP techniques. In Proceedings of the Eleventh International Joint Conference on Artificial Intelligence (IJCAI-89), pages 290--296, 1989.

....base and to compute the solutions grow linearly with n. n CPUTime Size KB Supporters 5 1:2s 83 25 6 1:5s 116 36 7 1:8s 155 49 8 2:1s 200 64 9 2:6s 251 81 10 3:1s 308 100 Table 1: Applying the ATMS to the minimal supporters problem It has been shown that an ATMS can be used as a constraint solver [ 8 ] . An example of the use of an ATMS as a constraint solver is the n queen problem. This problem is to place n queens on a n Theta n chessboard so that no queen dominates any other one. In order to specify the n queen problem, we introduce n 2 propositional variables; each one is associated ....

....graphs. This canonical form, which is amongst the most compact representations of Boolean functions that are currently known, has remarkable properties that give the system its efficiency. Our approach is quite different from the one followed by De Kleer who proposes an ATMS as a constraint solver [ 8 ] , since we use here a constraint solver developed for other purposes to build an ATMS. This ATMS has been integrated in the prototype version of a complex blast furnace computer aided piloting system [ 5 ] Within this system the RMS receives formulas from a reasoning system written in Kool [ 4 ....

J. de Kleer. Comparison of ATMS and CSP Techniques. In Proceedings of the 89 IJCAI Conference pages 290-296, Detroit, Michigan, 1989.

....that the values of the variables must simultaneously satisfy. The solution of CSP is a set of value assignments such that all the constraints are satisfied. Many approaches, as summarized in [1] have been developed to solve constraint problems such as Predicate Calculus [2] Propositional Logic [3], 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 ....

.... (which, in TMS, does not represent logical contradictions but rather states of the database explicitly declared to be undesirable) Based on this, McAllester proposed a Logic Based Truth Maintenance System (LTMS) 27] and de Kleer developed an AssumptionBased Truth Maintenance System (ATMS) [28, 3, 29]. Both TMS and LTMS pursue a single line of reasoning (i.e. a single context) at a time, and dependencydirected backtracking occurs when it is necessary to change the systems assumptions. In ATMS, alternating paths (i.e. multiple contexts) are maintained in parallel. The assumptions differ from ....

[Article contains additional citation context not shown here]

J. de Kleer, "A comparison of atms and csp techniques, " in Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, (Menlo Park, CA.), pp. 290--296, 1989.

....c is induced by a CSP (X; C) if it is satisfied by all the CSP solutions. This is usually called constraint propagation and has been formalized in various levels of so called local consistencies: arc consistency, path consistency, k consistency and has been related to ATMS nogood inference in [dK89] Adding enough induced constraints may even lead to backtrack free or backtrack bounded search [Fre88] 1.2 Dynamic constraint satisfaction problems Definition 1.4 A dynamic constraint satisfaction problem P is a sequence P 0 ; P ff ; of static CSPs each resulting from a change in ....

Johan de Kleer, A comparison of ATMS and CSP techniques, Proc. of the 11 th IJCAI (Detroit, MI), August 1989, pp. 290--296.

....DP itself. This could be done by improving the domain shortening after a choice is made and by performing an FC like domain exploration. To prove the equivalence of the two procedures we shall first recall in section 2. 1 how a CSP can be expressed as a SAT problem, thanks to de Kleer s translation [4]. In section 3, we will discuss two other procedures, the Quine algorithm of propositional calculus [8] and the Backtrack algorithm of CSPs. These procedures can be seen respectively as the Davis Putnam procedure and the Forward Checking procedure without any propagation. Once we will have ....

....relations can be seen as the allowed tuples by each clause. 2.1 Writing a CSP as SAT We first recall how anyCSP can be consideredas a SAT problem, then relate the CSP variables instantiations with propositional assignments and finally introduce the notion of compatible instantiation orders. In [4], de Kleer introduced an algorithm to express any CSP as a set of propositional clauses. We briefly recall it here. For each variable x i we introduce a proposition for each value a ij 2 D i . The propositional symbol x i a ij stands for the assertion x i = a ij . For each variable x i we write ....

J. de Kleer, `A Comparison of ATMS and CSP Techniques', in Proceedings IJCAI'89, (1989).

....processing in CSPs: 1. TMS work on problems encoded in propositional clauses. Obviously, CSPs (in the academic form) can be translated easily into this form. But the structure of the original problem (constraint graph, abstract notion of constraints and variables) is lost doing this translation [de Kleer, 1989]. Typical constraint processing techniques and heuristics rely heavily on this structure that is not available to a TMS. For instance, most real world applications of constraint processing techniques rely on the intensional representation of domains (e.g. by intervals) and constraints (e.g. by ....

Johan de Kleer. A comparison of ATMS and CSP techniques. In IJCAI--89: Proceedings of the International Joint Conference on Artificial Intelligence, pages 290--296, Detroit, MI, USA, 1989.

....that satisfies all the constraints. The classical approach consists of a solver that searches in the space of all the assignments for a correct one. We shall not enumerate the pros and cons of such an approach, as there is an extensive and rapidly growing literature that may be consulted (see [ Nadel, 1989 ] and the references quoted) Our approach is completely different from the previous one and arises from the desire to solve CSP in a distributed environment. Often it happens that the variables in a CSP may be associated in turn to a set of agents, representing some attribute of the agent. For ....

....or a partial solution but one needs to rationally justify the single steps that have produced the solution. 2 Constraint Satisfaction Problems Constraint Satisfaction Problems [ Mackworth, 1987, Ricci, 1990 ] arise in many areas of AI including: vision [ Waltz, 1975 ] truth maintenance systems [ de Kleer, 1989 ] scheduling [ Fox, 1987 ] graphics [ Borning et al. 1987 ] temporal reasoning [ Dechter et al. 1989 ] We refer the interested reader to the quoted papers as it is impossible to give even a partial account of the matter here. We shall often refer in the following to the 8 Queens problem, ....

Johan de Kleer. A comparison of the ATMS and CSP techniques. In Proceedings of the Eleventhth International Joint Conference on Artificial Intelligence, pages 290--296, 1989.

.... reutilisation de contraintes La premiere approche, developpee dans [60, 58] et designee sous le terme de Nogood Recording, s appuie sur une regle d inference simple, proche de la regle H5 utilisee par les ATMS, et sur laquelle s appuient egalement les algorithmes de filtrage de k consistance [19]. Il est ainsi possible de produire des nogoods au cours d une recherche classique a base de backtrack. Les nogoods produits sont des affectations partielles de l ensemble des variables qui ne peuvent en aucun cas etre prolongees en une solution. Ils sont utilises pour reduire l espace de ....

de Kleer (Johan). -- A comparison of ATMS and CSP techniques. In : Proc. of the 11 th IJCAI, pp. 290--296. -- Detroit, MI, aou t 1989.

....and can simply be deleted. A single pass on all variables and constraints is usually not sufficient and the process is performed iteratively until quiescence. 5 This process can be related to cutting plane generation in integer linear programming considering the combined results of [Hoo88] and [dK89] 6 It can be the case that some consistent assignment of n 1 variables can not be consistently extended to the n th variable. Satisfibility simply implies that some consistent assignment of k 1 variables do extend to a consistent assignment of all variables. Example: The CSP whose ....

J. de Kleer. A comparison of ATMS and CSP techniques. In Proc. of the 11 th IJCAI, pages 290--296, Detroit, MI, August 1989.

....scratch. So, if we add or retract constraints in a CSP and try to find a new solution after each modification with any of these algorithms, we will probably rediscover many identical failures at each satisfaction. Another approach, embodied in the ATMS and related to k consistency enforcing in [dK89], is to store, in a concise way, the whole frontier of the solution space explored along with justifications for its existence. However, the space needed may grow exponentially with the size of the problem, the complexity is far beyond satisfaction complexity [Pro90] and the services offered are ....

....enable some non globally consistent assignments to be discovered early. This is usually called constraint propagation and has been formalized in various levels of so called local consistency: arc consistency, path consistency, k consistency [Mac77] and has been related to ATMS nogood inference in [dK89]. 2.2 Dynamic constraint satisfaction problems Definition 2.4 A dynamic constraint satisfaction problem P is a sequence P 0 : P i : of static CSPs, each one resulting from a change in the preceding one [DD88] This change may be a restriction (a new constraint is imposed on a subset of ....

[Article contains additional citation context not shown here]

Johan de Kleer, A comparison of ATMS and CSP techniques, Proc. of the 11 th IJCAI (Detroit, MI), August 1989, pp. 290--296.

....correspondant au domaine de v ; si (A 1 [ f(v; val 1 )g; C 1 ) A i [ f(v; val i )g; C i ) A d [ f(v; val d )g; C d ) sont des nogoods, alors (A 1 [ A i [ A d ; C 1 [ C i [ C d [ fdom(v)g) est un nogood. Comme cela a ete note dans [SMI 88, KLE 89] ces differentes proprietes peuvent etre vues comme des particularisations et des applications au cadre CSP de la regle d hyper resolution suivante, valide en logique propositionnelle : fL 1 :M 1 ; L d :M d ; M 1 : M d Mg j= L 1 : L d M Il suffit pour cela de remplacer ....

DE KLEER J., A Comparison of ATMS and CSP Techniques. In : Proc. of IJCAI-89, p. 290--296, Detroit, MI, 1989.

....capabilities of the BMTMS are demonstrated. The evaluation results of the BMTMS, and conclusions are given in Section 6 and Section 7, respectively. 2 IDENTIFYING THE ISSUES OF CMS In this section, the drawbacks of the ATMS and the problems of CMS are demonstrated by using a a simple problem [ deK89 ] hereafter, the simple problem) shown in Figure 1. It has three variables, x 1 , x 2 , and x 3 . The domain of each variable is D 1 = fa; bg, D 2 = fc; d; eg, and D 3 = ff; gg, respectively. For a pair of variables, x i and x j , a constraint on them, C i;j , is given as the set of permissible ....

....A contradictory environment is called nogood. Each TMS node has a label, or a set of environments, under which the node is proved valid. The simple problem cannot encoded by ATMS itself, because it contains disjunctions and thus is not a Horn clause. The encoding techniques proposed by de Kleer [ deK89 ] is used for the encoding. The inference engine gives the following data to ATMS: DESIGN AND IMPLEMENTATION OF BMTMS ffl A propositional symbol, x i:v . A symbol x i:v means that a variable x i has a value v. Thus, x 1:a , x 1:b , x 2:c , x 2:d , x 2:e , x 3:f , x 3:g . ffl A set of ....

[Article contains additional citation context not shown here]

J. de Kleer. A Comparison of ATMS and CSP Techniques. In Proceedings of the Eleventh Internatioal Joint Conference on Artificial Intelligence (IJCAI), pages 290--296, 1989.

....processing in CSPs: 1. TMS work on problems encoded in propositional clauses. Obviously, CSPs (in the academic form) can be translated easily into this form. But the structure of the original problem (constraint graph, abstract notion of constraints and variables) is lost doing this translation [2]. Typical constraint processing techniques and heuristics rely heavily on this structure that is not available to a TMS. For instance, most real world applications of constraint processing techniques rely on the intensional representation of domains (e.g. by intervals) and constraints (e.g. by ....

Johan de Kleer. A comparison of ATMS and CSP techniques. In IJCAI--89: Proceedings of the International Joint Conference on Artificial Intelligence, pages 290--296, Detroit, MI, USA, 1989.

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