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On the size of good-for-games Rabin automata and its link with the memory in Muller games [article]

Antonio Casares, Thomas Colcombet, Karoliina Lehtinen
2022 arXiv   pre-print
In this paper, we look at good-for-games Rabin automata that recognise a Muller language (a language that is entirely characterised by the set of letters that appear infinitely often in each word).  ...  We establish that minimal such automata are exactly of the same size as the minimal memory required for winning Muller games that have this language as their winning condition.  ...  Acknowledgements We would like to thank Marthe Bonamy and Pierre Charbit for their help with graph theory.  ... 
arXiv:2204.11333v2 fatcat:wqcrwl6d5naf5o6moyciuqexfi

Universal Graphs and Good for Games Automata: New Tools for Infinite Duration Games [chapter]

Thomas Colcombet, Nathanaël Fijalkow
2019 Green Chemistry and Sustainable Technology  
We introduce for this purpose two new notions: good for small games automata and universal graphs.  ...  The first object, good for small games automata, induces a generic algorithm for solving games by reduction to safety games.  ...  We thank Pierre Ohlmann for many interesting discussions, and Marcin Jurdziński for his comments on an earlier draft of this paper.  ... 
doi:10.1007/978-3-030-17127-8_1 dblp:conf/fossacs/ColcombetF19 fatcat:rt2frqoeabd5bnhr72rauyebcy

From Logic to Games [chapter]

Igor Walukiewicz
2005 Lecture Notes in Computer Science  
It is universal in the sense that very game with a Muller condition can be reduced to a game with a parity condition [60] .  ...  This is partially due to the fact that timed-automata are not closed under complement and it is difficult to decide on some other good class of real-time properties.  ... 
doi:10.1007/11590156_5 fatcat:ps3dhgrvcnhabi6432n2rm5qrm

Computing the Width of Non-deterministic Automata

Denis Kuperberg, Anirban Majumdar
2018 Logical Methods in Computer Science  
Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly on any accepted input.  ...  The properties of GFG automata and their links with other models and algorithms (tree automata, Markov Decision Processes, efficient algorithms for parity games) are nowadays actively investigated [4,  ...  We thank the anonymous reviewers for their detailed feedback, and Nathalie Bertrand for helpful discussions.  ... 
doi:10.23638/lmcs-15(4:10)2019 fatcat:eip5jpqnmncifbphp6p5azhrem

Computing the Width of Non-deterministic Automata [article]

Denis Kuperberg, Anirban Majumdar
2019 arXiv   pre-print
Width generalises the notion of good-for-games (GFG) automata, that correspond to NFAs of width 1, and where an accepting run can be built on-the-fly on any accepted input.  ...  For coB\"uchi automata, this procedure can be used to compute either a deterministic automaton or a GFG one, and it is algorithmically more efficient in the last case.  ...  We thank the anonymous reviewers for their detailed feedback, and Nathalie Bertrand for helpful discussions.  ... 
arXiv:1811.00483v4 fatcat:yh35i52p4rgbvklkzpaeitsmne

Tighter Bounds for the Determinisation of Büchi Automata [chapter]

Sven Schewe
2009 Lecture Notes in Computer Science  
We can construct standard Rabin automata whose state-space is bilinear in the size of the input alphabet and the state-space of the Rabin transition automaton, or, for large input alphabets, contains approximately  ...  The introduction of an efficient determinisation technique for Büchi automata by Safra has been a milestone in automata theory.  ...  on the size of an ordinary deterministic Rabin automata on alphabets with l letters.  ... 
doi:10.1007/978-3-642-00596-1_13 fatcat:lso7d57zzzcz7oe4zyt37qotom

Index appearance record for transforming Rabin automata into parity automata [article]

Jan Křetínský and Tobias Meggendorfer and Clara Waldmann and Maximilian Weininger
2017 arXiv   pre-print
It leads to significantly smaller parity automata when compared to state-of-the-art approaches on complex formulae.  ...  Moreover, the experiments demonstrate the potential of our method for LTL synthesis, using LTL-to-Rabin translators.  ...  Finally, in order to estimate the effect on LTL synthesis more precisely, we shall link our tool chain to parity-game solvers and apply it to realistic case studies.  ... 
arXiv:1701.05738v1 fatcat:o2we4jkihvaazdnur7oalwow6q

Two-way cost automata and cost logics over infinite trees

Achim Blumensath, Thomas Colcombet, Denis Kuperberg, Paweł Parys, Michael Vanden Boom
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
The proof relies on an equivalence with a form of automata with counters called quasi-weak cost automata, as well as results about converting two-way alternating cost automata to one-way alternating cost  ...  Categories and Subject Descriptors Theory of computation [Automata over infinite objects] * The research leading to these results has received funding  ...  , for some correction function α that is independent of the size of the game.  ... 
doi:10.1145/2603088.2603104 dblp:conf/csl/BlumensathCKPB14 fatcat:27i2y2cnk5dtbb4zincmw43gvi

Higher-Order Model Checking: An Overview

Luke Ong
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
Advances have been made in determining the expressive power of recursion schemes and other higher-order families of generators, automata-theoretic characterisations of these generator families, and the  ...  Higher-order model checking is about the model checking of trees generated by recursion schemes. The past fifteen years or so have seen considerable progress in both theory and practice.  ...  Acknowledgements: The author is grateful to Takeshi Tsukada for helpful comments on the paper.  ... 
doi:10.1109/lics.2015.9 dblp:conf/lics/Ong15 fatcat:55bfxqlkuzhbtgmzc32m46ooku

Recursion Schemes, Collapsible Pushdown Automata and Higher-Order Model Checking [chapter]

Luke Ong
2013 Lecture Notes in Computer Science  
Collapsible pushdown automata are a generalisation of pushdown automata to higher-order stacks -which are iterations of stack of stacks -that contain symbols equipped with links.  ...  Recursion schemes are in essence the simply-typed lambda calculus with recursion, generated from first-order symbols.  ...  Acknowledgements Much of my work presented here is based on collaboration. I am grateful to all my collaborators for their help. Thanks are also due to EPSRC for financial support.  ... 
doi:10.1007/978-3-642-37064-9_3 fatcat:vmzogjyskfahbeklhyssyajvuy

Decidable Synthesis of Programs with Uninterpreted Functions [article]

Paul Krogmeier, Umang Mathur, Adithya Murali, P. Madhusudan, Mahesh Viswanathan
2019 arXiv   pre-print
We identify its precise complexity, which is doubly exponential in the set of program variables and linear in the size of the grammar.  ...  We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains.  ...  For example, the sequence of statements on the right defines a linked list of two elements with different keys.  ... 
arXiv:1910.09744v1 fatcat:2durnge54jdv7bkr6tj7l7plyu

Negotiating Cooperation Under Uncertainty: Communication in Noisy, Indefinitely Repeated Interactions

Fabian Dvorak, Sebastian Fehrler
2017 Social Science Research Network  
Two examples are teamwork arrangements in which workers repeatedly produce goods for each other, and cartels with repeated pricesetting by its members.  ...  We develop measures of strategic uncertainty and characterize the set of symmetric memory-one belief-free equilibria for the imperfect monitoring structures.  ...  on the production of a good for the other worker, and where whether the good is useful for the partner or not is a noisy signal of effort (Sekiguchi, 1997) .  ... 
doi:10.2139/ssrn.2986445 fatcat:hxx3uwhxjvaqvc36tofhdx3d2q

Evolution of mate-finding Allee effect in prey

Luděk Berec, Veronika Bernhauerová, Barbara Boldin
2018 Journal of Theoretical Biology  
Abstract We consider economic and social influences on the evolution of cooperative behaviour using a modified public goods game on a multiplex network as a model.  ...  cells on the nodes of the graph and letting them interact or replace each other via the links.  ...  In the proposed paper we analyse and outline open biological and technical problems on reliable and fast learning of objects, present the mathematical solution for some of these problems in the manner  ... 
doi:10.1016/j.jtbi.2017.12.024 pmid:29277599 fatcat:2p5kgwe6fffonblaccjhwlwvui

How to represent human behavior and decision making in Earth system models? A guide to techniques and approaches

Finn Müller-Hansen, Maja Schlüter, Michael Mäs, Rainer Hegselmann, Jonathan F. Donges, Jakob J. Kolb, Kirsten Thonicke, Jobst Heitzig
2017 Earth System Dynamics Discussions  
In the Anthropocene, humans have a critical impact on the Earth system and vice versa, which can generate complex feedback processes between social and ecological dynamics.  ...  We illustrate the main ingredients of modeling techniques with examples from land-use dynamics as one of the main drivers of environmental change bridging local to global scales.  ...  Most global models that describe human interactions with the Earth system we found in the literature are based on economic assumptions about the behavior of societies and are often only linked in a one-way  ... 
doi:10.5194/esd-2017-18 fatcat:dkdxjn5zbfgjfc7nsbb2uo7z3i

Abstracts of Working Papers in Economics

1994 Abstracts of Working Papers in Economics  
Walras (1954) suggests that we think of trade taking place at a family of trading posts, one for each pair of goods. In most economies we see few pairs of goods in active trade.  ...  The answer is relevant to problems in both game theory and econometrics, as we illustrate with examples.  ...  For finite games it is shown that given any fixed group of random orders, the linear operator on the whole space of games that assigns to each game its expected marginal contribution is symmetric with  ... 
doi:10.1017/s095100790000406x fatcat:yeczqgu23rfejdmwrke6csvgby
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