1,306 research outputs found
Deciding the Satisfiability of MITL Specifications
In this paper we present a satisfiability-preserving reduction from MITL
interpreted over finitely-variable continuous behaviors to Constraint LTL over
clocks, a variant of CLTL that is decidable, and for which an SMT-based bounded
satisfiability checker is available. The result is a new complete and effective
decision procedure for MITL. Although decision procedures for MITL already
exist, the automata-based techniques they employ appear to be very difficult to
realize in practice, and, to the best of our knowledge, no implementation
currently exists for them. A prototype tool for MITL based on the encoding
presented here has, instead, been implemented and is publicly available.Comment: In Proceedings GandALF 2013, arXiv:1307.416
On the Maximum Satisfiability of Random Formulas
Maximum satisfiability is a canonical NP-hard optimization problem that
appears empirically hard for random instances. Let us say that a Conjunctive
normal form (CNF) formula consisting of -clauses is -satisfiable if there
exists a truth assignment satisfying of all clauses
(observe that every -CNF is 0-satisfiable). Also, let denote a
random -CNF on variables formed by selecting uniformly and independently
out of all possible -clauses. It is easy to prove that for every
and every in , there is such that if , then the
probability that is -satisfiable tends to 0 as tends to
infinity. We prove that there exists a sequence such that if
then the probability that is
-satisfiable tends to 1 as tends to infinity. The sequence
tends to 0 exponentially fast in
- β¦