Commit 8e7a0cae authored by Quentin Aristote's avatar Quentin Aristote
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codensity parity games

parent 87a3a6a8
......@@ -237,4 +237,36 @@
publisher = {{Springer}},
abstract = {. In this paper we develop a new algorithm for deciding the winner in parity games, and hence also for the modal -calculus model checking. The design and analysis of the algorithm is based on a notion of game progress measures: they are witnesses for winning strategies in parity games. We characterize game progress measures as pre-fixed points of certain monotone operators on a complete lattice. As a result we get the existence of the least game progress measures and a straightforward way to compute them. The worst-case running time of our algorithm matches the best worst-case running time bounds known so far for the problem, achieved by the algorithms due to Browne et al., and Seidl. Our algorithm has better space complexity: it works in small polynomial space; the other two algorithms have exponential worst-case space complexity. 1 Introduction A parity game is an infinite path-forming game played by two players, player \# and player \#, on a graph with integer priorities assigned to...},
file = {/home/qaristote/Zotero/storage/YFXEX8BA/Jurdzinski - 2000 - Small Progress Measures for Solving Parity Games.pdf;/home/qaristote/Zotero/storage/HEPKDQ2E/summary.html}
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title = {Bisimulation, Modal Logic and Model Checking Games},
author = {Stirling, C.},
year = {1999},
month = jan,
volume = {7},
pages = {103--124},
publisher = {{Oxford Academic}},
issn = {1367-0751},
doi = {10.1093/jigpal/7.1.103},
abstract = {Abstract. We give a very brief introduction to how concurrent systems can be modelled within process calculi, as terms of an algebraic language whose behaviour},
file = {/home/qaristote/Zotero/storage/93D4SGA7/Stirling - 1999 - Bisimulation, modal logic and model checking games.pdf;/home/qaristote/Zotero/storage/7M36QIW4/681726.html},
journal = {Logic Journal of the IGPL},
language = {en},
number = {1}
title = {Abstraction, {{Up}}-to {{Techniques}} and {{Games}} for {{Systems}} of {{Fixpoint Equations}}},
author = {Baldan, Paolo and K{\"o}nig, Barbara and Padoan, Tommaso},
year = {2020},
month = mar,
abstract = {Systems of fixpoint equations over complete lattices, consisting of (mixed) least and greatest fixpoint equations, allow one to express a number of verification tasks such as model-checking of various kinds of specification logics or the check of coinductive behavioural equivalences. In this paper we develop a theory of approximation for systems of fixpoint equations in the style of abstract interpretation: a system over some concrete domain is abstracted to a system in a suitable abstract domain, with conditions ensuring that the abstract solution represents a sound/complete overapproximation of the concrete solution. Interestingly, up-to techniques, a classical approach used in coinductive settings to obtain easier or feasible proofs, can be interpreted as abstractions in a way that they naturally fit in our framework and extend to systems of equations. Additionally, relying on the approximation theory, we can provide a characterisation of the solution of systems of fixpoint equations over complete lattices in terms of a suitable parity game, generalising some recent work that was restricted to continuous lattices. The game view opens the way to the development of on-the-fly algorithms for characterising the solution of such equation systems.},
archivePrefix = {arXiv},
eprint = {2003.08877},
eprinttype = {arxiv},
file = {/home/qaristote/Zotero/storage/97A6VQ5S/Baldan et al. - 2020 - Abstraction, Up-to Techniques and Games for System.pdf;/home/qaristote/Zotero/storage/YX5NYYWR/2003.html},
journal = {arXiv:2003.08877 [cs]},
keywords = {Computer Science - Logic in Computer Science},
primaryClass = {cs}
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