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57
Propositional Independence: FormulaVariable Independence and Forgetting
 Journal of Artificial Intelligence Research
, 2003
"... Independence { the study of what is relevant to a given problem of reasoning { has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, ..."
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Cited by 55 (8 self)
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Independence { the study of what is relevant to a given problem of reasoning { has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic one. We show features and drawbacks of them. In particular, while the syntactic form of independence is computationally easy to check, there are cases in which things that intuitively are not relevant are not recognized as such. We also consider the problem of forgetting, i.e., distilling from a knowledge base only the part that is relevant to the set of queries constructed from a subset of the alphabet. While such process is computationally hard, it allows for a simpli  cation of subsequent reasoning, and can thus be viewed as a form of compilation: once the relevant part of a knowledge base has been extracted, all reasoning tasks to be performed can be simpli ed.
A sharp threshold in proof complexity
 PROCEEDINGS OF STOC 2001
, 2001
"... We give the first example of a sharp threshold in proof complexity. More precisely, we show that for any sufficiently small � and � � �, random formulas consisting of 2clauses and 3clauses, which are known to be unsatisfiable almost certainly, almost certainly require resolution and DavisPutnam ..."
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Cited by 52 (13 self)
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We give the first example of a sharp threshold in proof complexity. More precisely, we show that for any sufficiently small � and � � �, random formulas consisting of 2clauses and 3clauses, which are known to be unsatisfiable almost certainly, almost certainly require resolution and DavisPutnam proofs of unsatisfiability of exponential size, whereas it is easily seen that random formulas with 2clauses (and 3clauses) have linear size proofs of unsatisfiability almost certainly. A consequence of our result also yields the first proof that typical random 3CNF formulas at ratios below the generally accepted range of the satisfiability threshold (and thus expected to be satisfiable almost certainly) cause natural DavisPutnam algorithms to take exponential time to find satisfying assignments.
The impact of branching heuristics in propositional satisfiability algorithms
 In 9th Portuguese Conference on Artificial Intelligence (EPIA
, 1999
"... Abstract. This paper studies the practical impact of the branching heuristics used in Propositional Satisfiability (SAT) algorithms, when applied to solving realworld instances of SAT. In addition, different SAT algorithms are experimentally evaluated. The main conclusion of this study is that even ..."
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Cited by 43 (1 self)
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Abstract. This paper studies the practical impact of the branching heuristics used in Propositional Satisfiability (SAT) algorithms, when applied to solving realworld instances of SAT. In addition, different SAT algorithms are experimentally evaluated. The main conclusion of this study is that even though branching heuristics are crucial for solving SAT, other aspects of the organization of SAT algorithms are also essential. Moreover, we provide empirical evidence that for practical instances of SAT, the search pruning techniques included in the most competitive SAT algorithms may be of more fundamental significance than branching heuristics.
New WorstCase Upper Bounds for SAT
 Journal of Automated Reasoning
, 2000
"... In 1980 Monien and Speckenmeyer proved that satisfiability of a propositional formula consisting of K clauses (of arbitrary length) can be checked in time of the order 2^{K/3}. Recently Kullmann and Luckhardt proved the worstcase upper bound 2^{L/9}, where L is the length of the input formula. The ..."
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Cited by 35 (8 self)
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In 1980 Monien and Speckenmeyer proved that satisfiability of a propositional formula consisting of K clauses (of arbitrary length) can be checked in time of the order 2^{K/3}. Recently Kullmann and Luckhardt proved the worstcase upper bound 2^{L/9}, where L is the length of the input formula. The algorithms leading to these bounds are based on the splitting method which goes back to the Davis{Putnam procedure. Transformation rules (pure literal elimination, unit propagation etc.) constitute a substantial part of this method. In this paper we present a new transformation rule and two algorithms using this rule. We prove that these algorithms have the worstcase upper bounds 2^{0.30897K} and 2^{0.10299L}, respectively.
Setting 2 variables at a time yields a new lower bound for random 3SAT (Extended Abstract)
 STOC
, 2000
"... Let X be a set of n Boolean variables and denote by C(X) the set of all 3clauses over X, i.e. the set of all 8(3) possible disjunctions of three distinct, noncomplementary literais from variables in X. Let F(n, m) be a random 3SAT formula formed by selecting, with replacement, m clauses uniformly ..."
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Cited by 35 (4 self)
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Let X be a set of n Boolean variables and denote by C(X) the set of all 3clauses over X, i.e. the set of all 8(3) possible disjunctions of three distinct, noncomplementary literais from variables in X. Let F(n, m) be a random 3SAT formula formed by selecting, with replacement, m clauses uniformly at random from C(X) and taking their conjunction. The satisfiability threshold conjecture asserts that there exists a constant ra such that as n+ c¢, F(n, rn) is satisfiable with probability that tends to 1 if r < ra, but unsatisfiable with probability that tends to 1 if r:> r3. Experimental evidence suggests rz ~ 4.2. We prove rz> 3.145 improving over the previous best lower bound r3> 3.003 due to Frieze and Suen. For this, we introduce a satisfiability heuristic that works iteratively, permanently setting the value of a pair of variables in each round. The framework we develop for the analysis of our heuristic allows us to also derive most previous lower bounds for random 3SAT in a uniform manner and with little effort.
FDPLL – A FirstOrder DavisPutnamLogemanLoveland Procedure
 CADE17 – The 17th International Conference on Automated Deduction, volume 1831 of Lecture Notes in Artificial Intelligence
, 2000
"... Abstract. FDPLL is a directly lifted version of the wellknown DavisPutnamLogemanLoveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. nonground and comp ..."
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Cited by 33 (8 self)
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Abstract. FDPLL is a directly lifted version of the wellknown DavisPutnamLogemanLoveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. nonground and complementary literals now. The motivation for this lifting is to bring together successful firstorder techniques like unification and subsumption to the propositionally successful DPLL procedure. At the heart of the method is a new technique to represent firstorder interpretations, where a literal specifies truth values for all its ground instances, unless there is a more specific literal specifying opposite truth values. Based on this idea, the FDPLL calculus is developed and proven as strongly complete. 1
The Early History of Automated Deduction
 in Model Based Reasoning; Notes Workshop on ModelBased Reasoning
, 2001
"... this report. These are: 1. The one literal rule also known as the unit rule ..."
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Cited by 30 (0 self)
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this report. These are: 1. The one literal rule also known as the unit rule
Shape analysis through predicate abstraction and model checking
 In Proceedings of VMCAI
, 2003
"... Abstract. We propose a new framework, based on predicate abstraction and model checking, for shape analysis of programs. Shape analysis is used to statically collect information — such as possible reachability and sharing — about program stores. Rather than use a specialized abstract interpretation ..."
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Cited by 29 (1 self)
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Abstract. We propose a new framework, based on predicate abstraction and model checking, for shape analysis of programs. Shape analysis is used to statically collect information — such as possible reachability and sharing — about program stores. Rather than use a specialized abstract interpretation based on shape graphs, we instantiate a generic and automated abstraction procedure with shape predicates from a correctness property. This results in a predicatediscovery procedure that identifies predicates relevant for correctness, using an analysis based on weakest preconditions, and creates a finite state abstract program. The correctness property is then checked on the abstraction with a model checking tool. To enable this process, we calculate weakest preconditions for common shape properties, and present heuristics for accelerating convergence. Exploring abstract state spaces with model checkers enables one to tap into a wealth of techniques and highly optimized implementations for state space exploration, and to analyze properties that go beyond invariances. We illustrate this simple and flexible framework with the analysis of some “classical ” list manipulation programs, using our implementation of the abstraction algorithm, and the SPIN and COSPAN model checkers for state space exploration. 1
Applying the DavisPutnam procedure to nonclausal formulas
 In Proc. AI*IA'99, number 1792 in Lecture Notes in Arti Intelligence
, 1999
"... . Traditionally, the satisability problem for propositional logics deals with formulas in Conjunctive Normal Form (CNF). A typical way to deal with nonCNF formulas requires (i) converting them into CNF, and (ii) applying solvers usually based on the DavisPutnam (DP) procedure. A well known problem ..."
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Cited by 28 (7 self)
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. Traditionally, the satisability problem for propositional logics deals with formulas in Conjunctive Normal Form (CNF). A typical way to deal with nonCNF formulas requires (i) converting them into CNF, and (ii) applying solvers usually based on the DavisPutnam (DP) procedure. A well known problem of this solution is that the CNF conversion may introduce many new variables, thus greatly widening the space of assignments in which the DP procedure has to search in order to nd solutions. In this paper we present two variants of the DP procedure which overcome the problem outlined above. The idea underlying these variants is that splitting should occur only for the variables in the original formula. The CNF conversion methods employed ensure their correctness and completeness. As a consequence, we get two decision procedures for nonCNF formulas (i) which can exploit all the present and future sophisticated technology of current DP implementations, and (ii) whose space of assignments t...