Partial Quantifier Elimination

We consider the problem of Partial Quantifier Elimination (PQE). Given formula exists(X)[F(X,Y) & G(X,Y)], where F, G are in conjunctive normal form, the PQE problem is to find a formula F*(Y) such that F* & exists(X)[G] is logically equivalent to exists(X)[F & G]. We solve the PQE problem by generating and adding to F clauses over the free variables that make the clauses of F with quantified variables redundant. The traditional Quantifier Elimination problem (QE) is a special case of PQE where G is empty so all clauses of the input formula with quantified variables need to be made redundant. The importance of PQE is twofold. First, many problems are more naturally formulated in terms of PQE rather than QE. Second, in many cases PQE can be solved more efficiently than QE. We describe a PQE algorithm based on the machinery of dependency sequents and give experimental results showing the promise of PQE

Using Combinatorial Optimization Methods for Quantification Scheduling

Model checking is the process of verifying whether a model of a concurrent system satisfies a specified temporal property. Symbolic algorithms based on Binary Decision Diagrams (BDDs) have significantly increased the size of the models that can be verified. The main problem in symbolic model checking is the image computation problem, i.e., efficiently computing the successors or predecessors of a set of states. This paper is an in-depth study of the image computation problem. We analyze and evaluate several new heuristics, metrics, and algorithms for this problem. The algorithms use combinatorial optimization techniques such as hill climbing, simulated annealing, and ordering by recursive partitioning to obtain better results than was previously the case. Theoretical analysis and systematic experimentation are used to evaluate the algorithms

Using Combinatorial Optimization Methods for Quantification Scheduling

Model checking is the process of verifying whether a model o a coK452wG t system satisfies a specified tempomp property. Symbolic algoP90wG basedo n Binary Decisio Diagrams (BDDs) have significantly increased the sizeo the mo dels that can be verified. The mainprow42 in symbo licmo del checking is the image computVN7B problem, i.e., e#ciently co4j97Kw the successoK o r predecesso5 o f a seto f states. This paper is an in-depth studyo the imagecoew5O7j5w pro4Kj4 We analyze and evaluate several newheuristics, metrics, and algo979wG fo thisprow0P0 The algoj25wG use co binato0wG oto0wG4Pj2 techniques such as hill climbing,simulat d annealing,andordering by recursive partWBBVN3F to oO0 better results than was previo4wG the case. Theo70wG42 analysis and systematic experimentatio are used to evaluate the algoPKwG4