Simple Fixpoint Iteration To Solve Parity Games

A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the many algorithms for parity games. We now consider a method of solving parity games by means of a naive fixpoint iteration. Several fixpoint algorithms for parity games have been proposed in the literature. In this work, we introduce an algorithm that relies on the notion of a distraction. The idea is that this offers a novel perspective for understanding parity games. We then show that this algorithm is in fact identical to two earlier published fixpoint algorithms for parity games and thus that these earlier algorithms are the same. Furthermore, we modify our algorithm to only partially recompute deeper fixpoints after updating a higher set and show that this modification enables a simple method to obtain winning strategies. We show that the resulting algorithm is simple to implement and offers good performance on practical parity games. We empirically demonstrate this using games derived from model-checking, equivalence checking and reactive synthesis and show that our fixpoint algorithm is the fastest solution for model-checking games.Comment: In Proceedings GandALF 2019, arXiv:1909.0597

Building Strategies into QBF Proofs

Strategy extraction is of great importance for quantified Boolean formulas (QBF), both in solving and proof complexity. So far in the QBF literature, strategy extraction has been algorithmically performed from proofs. Here we devise the first QBF system where (partial) strategies are built into the proof and are piecewise constructed by simple operations along with the derivation. This has several advantages: (1) lines of our calculus have a clear semantic meaning as they are accompanied by semantic objects; (2) partial strategies are represented succinctly (in contrast to some previous approaches); (3) our calculus has strategy extraction by design; and (4) the partial strategies allow new sound inference steps which are disallowed in previous central QBF calculi such as Q-Resolution and long-distance Q-Resolution. The last item (4) allows us to show an exponential separation between our new system and the previously studied reductionless long-distance resolution calculus. Our approach also naturally lifts to dependency QBFs (DQBF), where it yields the first sound and complete CDCL-style calculus for DQBF, thus opening future avenues into CDCL-based DQBF solving

Proceedings of the 2008 Oxford University Computing Laboratory student conference.

This conference serves two purposes. First, the event is a useful pedagogical exercise for all participants, from the conference committee and referees, to the presenters and the audience. For some presenters, the conference may be the first time their work has been subjected to peer-review. For others, the conference is a testing ground for announcing work, which will be later presented at international conferences, workshops, and symposia. This leads to the conference's second purpose: an opportunity to expose the latest-and-greatest research findings within the laboratory. The fourteen abstracts within these proceedings were selected by the programme and conference committee after a round of peer-reviewing, by both students and staff within this department

Whitworth College Bulletin 1987-1989

https://digitalcommons.whitworth.edu/whitworthcatalogs/1077/thumbnail.jp

Whitworth University Catalog 2017-2018

https://digitalcommons.whitworth.edu/whitworthcatalogs/1095/thumbnail.jp

Hard QBFs for Merge Resolution

We prove the first 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 resolution systems in the literature, proofs in MRes consist of resolution steps together with information on countermodels, which are syntactically stored in the proofs as merge maps. As demonstrated in [Olaf Beyersdorff et al., 2020], this makes MRes quite powerful: it has strategy extraction by design and allows short proofs for formulas which are hard for classical QBF resolution systems. Here we show the first exponential lower bounds for MRes, thereby uncovering limitations of MRes. Technically, the results are either transferred from bounds from circuit complexity (for restricted versions of MRes) or directly obtained by combinatorial arguments (for full MRes). Our results imply that the MRes approach is largely orthogonal to other QBF resolution models such as the QCDCL resolution systems QRes and QURes and the expansion systems ?Exp+Res and IR

Whitworth University Catalog 2020-2021

https://digitalcommons.whitworth.edu/whitworthcatalogs/1098/thumbnail.jp

Whitworth University Catalog 2019-2020

https://digitalcommons.whitworth.edu/whitworthcatalogs/1097/thumbnail.jp

Whitworth University Catalog 2018-2019

https://digitalcommons.whitworth.edu/whitworthcatalogs/1096/thumbnail.jp