English
Related papers

Related papers: Semi-Algebraic Proof Systems for QBF

200 papers

Q-resolution is a proof system for quantified Boolean formulas (QBFs) in prenex conjunctive normal form (PCNF) which underlies search-based QBF solvers with clause and cube learning (QCDCL). With the aim to derive and learn stronger clauses…

Logic in Computer Science · Computer Science 2016-06-15 Florian Lonsing , Uwe Egly , Martina Seidl

We present an experimental study of the effects of quantifier alternations on the evaluation of quantified Boolean formula (QBF) solvers. The number of quantifier alternations in a QBF in prenex conjunctive normal form (PCNF) is directly…

Logic in Computer Science · Computer Science 2018-09-05 Florian Lonsing , Uwe Egly

Dependency quantified Boolean formulas (DQBF) is a logic admitting existential quantification over Boolean functions, which allows us to elegantly state synthesis problems in verification such as the search for invariants, programs, or…

Logic in Computer Science · Computer Science 2019-05-08 Leander Tentrup , Markus N. Rabe

Stochastic Barrier Functions (SBFs) certify the safety of stochastic systems by formulating a functional optimization problem, which state-of-the-art methods solve using Sum-of-Squares (SoS) polynomials. This work focuses on polynomial SBFs…

Optimization and Control · Mathematics 2025-06-12 Peter Amorese , Morteza Lahijanian

In recent years, expansion-based techniques have been shown to be very powerful in theory and practice for solving quantified Boolean formulas (QBF), the extension of propositional formulas with existential and universal quantifiers over…

Logic in Computer Science · Computer Science 2018-10-08 Roderick Bloem , Nicolas Braud-Santoni , Vedad Hadzic , Uwe Egly , Florian Lonsing , Martina Seidl

This paper illustrates the relationship between boolean propositional algebra and semirings, presenting some results of partial ordering on boolean propositional algebras, and the necessary conditions to represent a boolean propositional…

Rings and Algebras · Mathematics 2009-06-26 Mahesh Rudrachar , Shrisha Rao , Amit Raj

Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time…

Logic in Computer Science · Computer Science 2021-05-20 Fedor Part , Neil Thapen , Iddo Tzameret

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

Logic in Computer Science · Computer Science 2023-10-20 Alexander V. Gheorghiu , David J. Pym

Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as…

Artificial Intelligence · Computer Science 2011-11-04 E. Giunchiglia , M. Narizzano , A. Tacchella

Term-resolution provides an elegant mechanism to prove that a quantified Boolean formula (QBF) is true. It is a dual to Q-resolution (also referred to as clause-resolution) and is practically highly important as it enables certifying…

Logic in Computer Science · Computer Science 2017-04-05 Mikoláš Janota

Quantitative Bipolar Argumentation Frameworks (QBAFs) provide an alternative approach to computing argument acceptability in Bipolar Argumentation Frameworks (BAFs). Each argument is assigned an initial strength, which is then updated to a…

Artificial Intelligence · Computer Science 2026-05-05 Gianvincenzo Alfano , Sergio Greco , Lucio La Cava , Francesco Parisi , Irina Trubitsyna

Large complexity classes, like the exponential time hierarchy, received little attention in terms of finding complete problems. In this work a generalization of propositional logic is investigated which fills this gap with the introduction…

Computational Complexity · Computer Science 2016-05-30 Martin Lück

The theory of quasi-Lie systems, i.e. systems of first order ordinary differential equations which can be related via a generalised flow to Lie systems, is extended to systems of partial differential equations and its applications to…

Analysis of PDEs · Mathematics 2024-11-04 Jose F. Carinena , Janusz Grabowski , Javier de Lucas

Graph generation and enumeration problems often require handling equivalent graphs -- those that differ only in vertex labeling. We study how to extend SAT Modulo Symmetries (SMS), a framework for eliminating such redundant graphs, to…

Logic in Computer Science · Computer Science 2025-02-24 Mikoláš Janota , Markus Kirchweger , Tomáš Peitl , Stefan Szeider

Strong algebraic proof systems such as IPS (Ideal Proof System; Grochow-Pitassi [GP18]) offer a general model for deriving polynomials in an ideal and refuting unsatisfiable propositional formulas, subsuming most standard propositional…

Computational Complexity · Computer Science 2024-12-31 Tuomas Hakoniemi , Nutan Limaye , Iddo Tzameret

Algebraic quantization scheme has been proposed as an extension of the Dirac quantization scheme for constrained systems. Semi-classical states for constrained systems is also an independent and important issue, particularly in the context…

Quantum Physics · Physics 2007-05-23 G. Date , Parampreet Singh

This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…

Logic in Computer Science · Computer Science 2015-07-01 Assia Mahboubi , Cyril Cohen

These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…

Logic · Mathematics 2014-02-10 Matteo Viale , Giorgio Audrito , Silvia Steila

We present version 2.0 of QRATPre+, a preprocessor for quantified Boolean formulas (QBFs) based on the QRAT proof system and its generalization QRAT+. These systems rely on strong redundancy properties of clauses and universal literals.…

Logic in Computer Science · Computer Science 2019-07-03 Florian Lonsing , Uwe Egly

We prove the first genuine QBF proof size lower bounds for the proof system Merge Resolution (MRes [Olaf Beyersdorff et al., 2020]), a refutational proof system for prenex quantified Boolean formulas (QBF) with a CNF matrix. Unlike most QBF…

Computational Complexity · Computer Science 2024-09-13 Olaf Beyersdorff , Joshua Blinkhorn , Meena Mahajan , Tomáš Peitl , Gaurav Sood