We prove that, with high probability, the space complexity of refuting a random unsatisfiable boolean formula in -CNF on variables and clauses is .

2QBF is a special form ∀x∃y.φ of the quantified Boolean formula (QBF) restricted to only two quantification layers, where φ is a quantifier-free formula. Despite its restricted form, it provides a framework for a wide range of applications, such as artificial intelligence, graph theory, synthesis, etc. In this work, we overview two main 2QBF challenges in terms of solving and certification. We ...

We parameterize countable locally standard Boolean measure algebras by pairs of a Steinitz number and real greater or equal to [Formula: see text] This is an analog the theorems Dixmier Baranov.

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of canalizing functions to other classes of functions with respect to their evolutionary plausibility as emergent control rules in genetic regulatory systems, it ...

We show that the following problem is EXP-complete: given a rational v and a two player, zero-sum Boolean gameG determine whether the value of G is at least v. The proof is via a translation of the proof of the same result for Boolean circuit games in [1]. 1 Preliminaries We will be using the encoding of [2] to replicate the proof of [1]. A familiarity with [2] will make the proof much easier t...

We aim to understand inherent reasons for lower bounds for QBF proof systems, and revisit and compare two previous approaches in this direction. The first of these relates size lower bounds for strong QBF Frege systems to circuit lower bounds via strategy extraction (Beyersdorff & Pich, LICS’16). Here we show a refined version of strategy extraction and thereby for any QBF proof system obtain a...

The best currently available solvers for quantified Boolean formulas (QBFs) process their input in prenex form, i.e., all the quantifiers are to appear in the prefix of the formula separated from the purely propositional part representing the matrix. However, in many QBFs deriving from applications, the propositional part is intertwined with the quantifiers structure. In this paper, we show tha...

Abstract. We provide an empirical evaluation of one of the main test sets that is currently in use for testing modal satisfiability solvers, viz. the random modal QBF test set. We first discuss some of the background underlying the test set, and then evaluate the test set using criteria set forth by Horrocks, Patel-Schneider, and Sebastiani. We also present some guidelines for the use of the te...

Q-resolution and its variations provide the underlying proof systems for the DPLL-based QBF solvers. While (long-distance) Q-resolution models a conflict driven clause learning (CDCL) QBF solver, it is not known whether the inverse is also true. This paper provides a negative answer to this question. This contrasts with SAT solving, where CDCL solvers have been shown to simulate resolution.

Inspired by recent work on parallel SAT solving, we present a lightweight approach for solving quantified Boolean formulas (QBFs) in parallel. In particular, our approach uses a sequential state-of-the-art QBF solver to evaluate subformulas in working processes. It abstains from globally exchanging information between the workers, but keeps learnt information only locally. To this end, we equip...