Results 1  10
of
22
New Upper Bounds for Maximum Satisfiability
 Journal of Algorithms
, 1999
"... The (unweighted) Maximum Satisfiability problem (MaxSat) is: given a boolean formula in conjunctive normal form, find a truth assignment that satisfies the most number of clauses. This paper describes exact algorithms that provide new upper bounds for MaxSat. We prove that MaxSat can be solved i ..."
Abstract

Cited by 38 (2 self)
 Add to MetaCart
(Show Context)
The (unweighted) Maximum Satisfiability problem (MaxSat) is: given a boolean formula in conjunctive normal form, find a truth assignment that satisfies the most number of clauses. This paper describes exact algorithms that provide new upper bounds for MaxSat. We prove that MaxSat can be solved in time O(F  1.3803 K ), where F  is the length of a formula F in conjunctive normal form and K is the number of clauses in F . We also prove the time bounds O(F 1.3995 k ), where k is the maximum number of satisfiable clauses, and O(1.1279 F  ) for the same problem. For Max2Sat this implies a bound of O(1.2722 K ). # An extended abstract of this paper was presented at the 26th International Colloquium on Automata, Languages, and Programming (ICALP'99), LNCS 1644, SpringerVerlag, pages 575584, held in Prague, Czech Republic, July 1115, 1999. + Supported by a Feodor Lynen fellowship (1998) of the Alexander von HumboldtStiftung, Bonn, and the Center for Discrete Ma...
Restoring Satisfiability or Maintaining Unsatisfiability by finding small Unsatisfiable Subformulae
 In LICS Workshop on Theory and Applications of Satisfiability Testing
, 2001
"... In several applicative fields, the generic system or structure to be designed can be encoded as a CNF formula, which should have a welldefined satisfiability property (either to be satisfiable or to be unsatisfiable). Within a complete solution frame work, we develop an heuristic procedure which i ..."
Abstract

Cited by 32 (2 self)
 Add to MetaCart
(Show Context)
In several applicative fields, the generic system or structure to be designed can be encoded as a CNF formula, which should have a welldefined satisfiability property (either to be satisfiable or to be unsatisfiable). Within a complete solution frame work, we develop an heuristic procedure which is able, for unsatisfiable instances, to locate a set of clauses causing unsatisfiability. That corresponds to the part of the system that we respectively need to redesign or to keep when we respectively want a satisfiable or unsatisfiable formula. Such procedure can guarantee to find an unsatisfiable subformula, and is aimed to find an approximation of a minimum unsatisfiable subformula. Successful results on both real life data collecting problems and Dimacs problems are presented.
Approximating Minimal Unsatisfiable Subformulae by Means of Adaptive Core Search
 Discrete Applied Mathematics
, 2002
"... The paper is concerned with the relevant practical problem of selecting a small unsatisfiable subset of clauses inside an unsatisfiable CNF formula. Moreover, it deals with the algorithmic problem of improving an enumerative (DPLLstyle) approach to SAT, in order to overcome some structural defects ..."
Abstract

Cited by 29 (1 self)
 Add to MetaCart
(Show Context)
The paper is concerned with the relevant practical problem of selecting a small unsatisfiable subset of clauses inside an unsatisfiable CNF formula. Moreover, it deals with the algorithmic problem of improving an enumerative (DPLLstyle) approach to SAT, in order to overcome some structural defects of such approach. Within a complete solution framework, we are able to evaluate the di#culty of each clause, by analyzing the history of the search. Such clause hardness evaluation is used in order to rapidly select an unsatisfiable subformula (of the given CNF) which is a good approximation of a minimal unsatisfiable subformula (MUS). Unsatisfiability is proved by solving only such subformula. Very small unsatisfiable subformulae are detected inside famous Dimacs unsatisfiable problems and in real world problems. Comparison with the very e#cient solver SATO 3.2 used as a stateoftheart DPLL procedure (disabling learning of new clauses) shows the e#ectiveness of such enumeration guide.
GRASP with pathrelinking for the weighted MAXSAT problem
 ACM Journal of Experimental Algorithmics
, 2006
"... A GRASP with path relinking for finding goodquality solutions of the weighted maximum satisfiability problem (MAXSAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multistart metaheuristic, where, at each iteration, locally optimal solutions are ..."
Abstract

Cited by 17 (12 self)
 Add to MetaCart
A GRASP with path relinking for finding goodquality solutions of the weighted maximum satisfiability problem (MAXSAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multistart metaheuristic, where, at each iteration, locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted MAXSAT instances. Path relinking is a procedure used to intensify the search around goodquality isolated solutions that have been produced by the GRASP heuristic. Experimental comparison of the pure GRASP (without path relinking) and the GRASP with path relinking illustrates the effectiveness of path relinking in decreasing the average time needed to find a goodquality solution for the weighted maximum satisfiability problem.
Improved exact algorithms for MAXSAT
 Discrete Applied Mathematics
, 2002
"... In this paper we present improved exact and parameterized algorithms for the maximum satisfiability problem. In particular, we give an algorithm that computes a truth assignment for a boolean formula F satisfying the maximum number of clauses in time O(1.3247 m F ), where m is the number of clause ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
(Show Context)
In this paper we present improved exact and parameterized algorithms for the maximum satisfiability problem. In particular, we give an algorithm that computes a truth assignment for a boolean formula F satisfying the maximum number of clauses in time O(1.3247 m F ), where m is the number of clauses in F, and F  is the sum of the number of literals appearing in each clause in F. Moreover, given a parameter k, we give an O(1.3695 k + F ) parameterized algorithm that decides whether a truth assignment for F satisfying at least k clauses exists. Both algorithms improve the previous best algorithms by Bansal and Raman for the problem. Key words. maximum satisfiability, exact algorithms, parameterized algorithms. 1
On exact selection of minimally unsatisfiable subformulae
 Annals of Mathematics and Artificial Intelligence
, 2005
"... ..."
(Show Context)
Worstcase study of local search for MaxkSAT
 Discrete Appl. Math
, 2003
"... ..."
(Show Context)
Bounded Rationality in Repeated Games and Mechanism Design for Agents in Computational Settings
, 2000
"... In Part I, we study bounded rationality in repeated twoperson zerosum games. First we investigate infinitely repeated games in which both players are restricted to pure strategies that can be executed on a finite automaton. In particular, we provide an upper bound on the number of states that Play ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
In Part I, we study bounded rationality in repeated twoperson zerosum games. First we investigate infinitely repeated games in which both players are restricted to pure strategies that can be executed on a finite automaton. In particular, we provide an upper bound on the number of states that Player 2 needs to defeat Player 1 when Player 1 is restricted to simple cycles of length m. Next we argue that the finite automaton approach to bounded rationality is not satisfactory. As an alternative, we propose limiting the number of strategies available to the players. We provide a thorough study of finitely repeatedly zero sum games in which Player 1 is restricted to mixing over a fixed number of pure strategies while Player 2 is unrestricted. We describe an optimal set of pure strategies for Player 1 and a method for describing these strategies such that any strategy from this set can be efficiently executed given its description. We develop upper and lower bounds on the value of these games and discuss how the value is related to the strategic entropy function defined by Neyman and Okada (1999). Finally, we show that an approximately optimal set can be produced in time which is linear in the size of the set. This set achieves a total expected payoff that is within an additive constant of the optimal.
Learning while Optimizing an Unknown Fitness Surface ⋆
"... Abstract. This paper is about Reinforcement Learning (RL) applied to online parameter tuning in Stochastic Local Search (SLS) methods. In particular a novel application of RL is considered in the Reactive Tabu Search (RTS) method, where the appropriate amount of diversification in prohibitionbased ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract. This paper is about Reinforcement Learning (RL) applied to online parameter tuning in Stochastic Local Search (SLS) methods. In particular a novel application of RL is considered in the Reactive Tabu Search (RTS) method, where the appropriate amount of diversification in prohibitionbased (Tabu) local search is adapted in a fast online manner to the characteristics of a task and of the local configuration. We model the parametertuning policy as a Markov Decision Process where the states summarize relevant information about the recent history of the search, and we determine a nearoptimal policy by using the Least Squares Policy Iteration (LSPI) method. Preliminary experiments on Maximum Satisfiability (MAXSAT) instances show very promising results indicating that the learnt policy is competitive with previously proposed reactive strategies. 1 Reinforcement Learning and Reactive Search Reactive Search (RS) [1–3] advocates the integration of subsymbolic machine
MAX2SAT: How Good is Tabu Search in the WorstCase?
, 2004
"... Tabu search algorithms are amongst the most successful local search based methods for the maximum satisfiability problem. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Tabu search algorithms are amongst the most successful local search based methods for the maximum satisfiability problem.