We analyze the performance of various clause selection heuristics for saturating first-order theorem provers. These heuristics include elementary first-in/fist-out and symbol counting, but also interleaved heuristics and a complex heuristic with goal-directed components. We can both confirm and dispel some parts of developer folklore. Key results include: (1) Simple symbol counting heuristics b...

As satisfiability (SAT) solver performance has improved, so has their complexity, which make it more likely that SAT solvers contain bugs. One important source of increased complexity is clause sharing in parallel SAT solvers. SAT solvers can emit a proof of unsatisfiability to gain confidence that their results are correct. Such proofs must contain deletion information in order to check them e...

a contractual relationship is commonly based on statements, expectations, acts and omissions out of which some will, and others will not, give rise to contractual obligations. to avoid uncertainty as to what is agreed, the contract parties often enter into a written contract that is supposed to express the final agreement between them and prevent the parties from relying on rights and obligatio...

The paper presents a new resource light flexible method for clause alignment which combines the Gale-Church algorithm with internally collected textual information. The method does not resort to any pre-developed linguistic resources which makes it very appropriate for resource light clause alignment. We experiment with a combination of the method with the original Gale-Church algorithm (1993) ...

In this paper, we investigate condensation of a clause. First, we extend a substitution graph introduced by Scheffer et al. (1996) to a total matcher graph. Then, we give a correct proof of the relationship between subsumption and the existence of cliques in a total matcher graph. Next, we introduce the concept of width of a clique in a total matcher graph. As a corollary of the above relations...

English sentences such as I consider John smart have long presented analytic ambiguity between a “small clause” analysis and a “predication” analysis, and the apparently equivalent sentence-type in Greek, e.g. presents similar problems. Here it is argued that additional evidence from each language, involving constructions that are sensitive to the thematicity of an object NP, shows that these s...

Experimentation of new algorithms is the usual companion section of papers dealing with SAT. However, the behavior of those algorithms is so unpredictable that even strong experiments (hundreds of benchmarks, dozen of solvers) can be still misleading. We present here a set of experiments of very small changes of a canonical Conflict Driven Clause Learning (CDCL) solver and show that even very c...

–Conflict-Driven Clause Learning: – are believed to be well-known: ∗ They embed dynamic heuristics [6, 3], learning [7], restarts [4, 1] and lazy data structures [6]. ∗ (efficient) SAT Solvers can be written from scratch in less than a thousand lines of code. – are not so well-known: ∗Who really understand the underlying mechanisms? ∗No real experimental studies: Progresses have been made with ...

We give an exact deterministic algorithm for MAX-SAT. On input CNF formulas with constant clause density (the ratio of the number of clauses to the number of variables is a constant), this algorithm runs in O(c) time where c < 2 and n is the number of variables. Worst-case upper bounds for MAX-SAT less than O(2) were previously known only for k-CNF formulas and for CNF formulas with small claus...