Tomas Peitl | AC Group | TU Wien

Graph Choosability via SAT: Beyond the Nullstellensatz

Thu, 01 Jan 2026 00:00:00 +0000

Smart Cubing for Graph Search: A Comparative Study

Thu, 01 Jan 2026 00:00:00 +0000

Strong (D)QBF Dependency Schemes via Pure Paths with Applications to Proof Checking

Thu, 01 Jan 2026 00:00:00 +0000

Better Extension Variables in DQBF via Independence

Wed, 01 Jan 2025 00:00:00 +0000

Breaking Symmetries in Quantified Graph Search: A Comparative Study

Wed, 01 Jan 2025 00:00:00 +0000

ASK-SAT: Alternating Symmetry-Breaking Combinatorial Search with SAT

Mon, 01 Jan 2024 00:00:00 +0000

Project Acronym: ASK-SAT (Alternating Symmetry-Breaking Combinatorial Search with SAT)

Funding organization: Austrian Science Fund (FWF)

Project number: P 36688

Grant DOI: 10.55776/P36688

Project Team

Topic

Many unsolved problems in discrete mathematics and extremal combinatorics can be stated as whether a combinatorial object with a particular property and size exists.

The project focuses on developing novel methods for answering such questions using the innovative Satisfiability Modulo Symmetries (SMS) technique. This approach departs from traditional exhaustive search strategies by dynamically identifying and excluding redundant sub-configurations, thus streamlining the search process while utilizing the power of solvers for the propositional satisfiability problem (SAT).

The project aims to extend the capabilities of SMS to effectively tackle the existence of objects whose defining property requires alternating quantifiers, which present unique challenges beyond the scope of conventional SAT methods. This involves integrating advanced computational tools, including quantified Boolean formulas and symmetry-reasoning technologies.

Through this research, the project aspires to advance the fields of automated reasoning and discrete mathematics.

Software

The software tool developed through the project is available via GitHub, the documentation via Read the Docs.

Hard QBFs for Merge Resolution

Mon, 01 Jan 2024 00:00:00 +0000

QCDCL with cube learning or pure literal elimination - What is best?

Mon, 01 Jan 2024 00:00:00 +0000

Should Decisions in QCDCL Follow Prefix Order?

Mon, 01 Jan 2024 00:00:00 +0000

Small unsatisfiable k-CNFs with bounded literal occurrence

Mon, 01 Jan 2024 00:00:00 +0000

Variable Dependencies of Quantified Boolean Formulas

Mon, 01 Jan 2024 00:00:00 +0000

Funding Organisation: The Austrian Science Fund, FWF
Project Number: FWF P 27721

Project Team

Friedrich Slivovsky
Tomas Peitl
Stefan Szeider (Professor, Principal Investigator)

Topic

The satisfiability problem of Quantified Boolean Formulas (QBF) offers succinct encodings for hard problems arising in areas such as formal verification and planning. This research project explores new ways to leverage independence of variables for QBF. The nesting of existential and universal quantifiers in Quantified Boolean Formulas can generate variable dependencies that are a serious obstacle to lifting successful techniques from propositional satisfiability to QBF. In some cases one can identify a variable dependency as spurious and conclude that the corresponding variables are in fact independent. This information can be used to significantly improve the performance of decision procedures, but deciding whether variables are independent is a highly intractable problem in itself.

The aim of this project is three-fold: (A) to advance the state of the art in detecting variable independence by developing new theory and improved algorithms for currently used methods; (B) to find new approaches to detecting and harnessing variable independence; (C) to extend the scope of successful techniques from QBF to more general problems.

Software

Research under Theme (B) has lead to the development of Qute (GitHub), a dependency learning QBF solver. Qute placed 3rd in the PCNF track and 4th in the Prenex non-CNF track of QBFEVAL'17.

A SAT Solver's Opinion on the Erdős-Faber-Lovász Conjecture

Sun, 01 Jan 2023 00:00:00 +0000

Are Hitting Formulas Hard for Resolution?

Sun, 01 Jan 2023 00:00:00 +0000

Co-Certificate Learning with SAT Modulo Symmetries

Sun, 01 Jan 2023 00:00:00 +0000

Hardness Characterisations and Size-Width Lower Bounds for QBF Resolution

Thu, 01 Sep 2022 00:00:00 +0000

QCDCL with Cube Learning or Pure Literal Elimination - What is Best?

Sat, 01 Jan 2022 00:00:00 +0000

Should Decisions in QCDCL Follow Prefix Order?

Sat, 01 Jan 2022 00:00:00 +0000

Davis and Putnam Meet Henkin: Solving DQBF with Resolution

Fri, 01 Jan 2021 00:00:00 +0000

Davis and Putnam Meet Henkin: Solving DQBF with Resolution

Fri, 01 Jan 2021 00:00:00 +0000

Finding the Hardest Formulas for Resolution

Fri, 01 Jan 2021 00:00:00 +0000

Finding the Hardest Formulas for Resolution (Extended Abstract)

Fri, 01 Jan 2021 00:00:00 +0000

Strong (D)QBF Dependency Schemes via Implication-free Resolution Paths

Fri, 01 Jan 2021 00:00:00 +0000

Finding the Hardest Formulas for Resolution

Wed, 01 Jan 2020 00:00:00 +0000

Finding the Hardest Formulas for Resolution

Wed, 01 Jan 2020 00:00:00 +0000

Fixed-Parameter Tractability of Dependency QBF with Structural Parameters

Wed, 01 Jan 2020 00:00:00 +0000

Fixed-Parameter Tractability of Dependency QBF with Structural Parameters

Wed, 01 Jan 2020 00:00:00 +0000

Hard QBFs for Merge Resolution

Wed, 01 Jan 2020 00:00:00 +0000

Strong (D)QBF Dependency Schemes via Tautology-free Resolution Paths

Wed, 01 Jan 2020 00:00:00 +0000

Combining Resolution-Path Dependencies with Dependency Learning

Tue, 01 Jan 2019 00:00:00 +0000

Combining Resolution-Path Dependencies with Dependency Learning

Tue, 01 Jan 2019 00:00:00 +0000

Dependency Learning for QBF

Tue, 01 Jan 2019 00:00:00 +0000

Long-Distance Q-Resolution with Dependency Schemes

Tue, 01 Jan 2019 00:00:00 +0000

Proof Complexity of Fragments of Long-Distance Q-resolution

Tue, 01 Jan 2019 00:00:00 +0000

Proof Complexity of Fragments of Long-Distance Q-resolution

Tue, 01 Jan 2019 00:00:00 +0000

Polynomial-Time Validation of QCDCL Certificates