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Observations on determinization of Büchi automata

Christoph Schulte Althoff, Wolfgang Thomas, Nico Wallmeier
2006 Theoretical Computer Science  
The two determinization procedures of Safra and Muller-Schupp for Büchi automata are compared, based on an implementation in a program called OmegaDet.  ...  Acknowledgement We thank Detlef Kähler for his presentation of [14] in our seminar and remarks on a preliminary version of the paper; we relied on his work at several places.  ...  The second author acknowledges fruitful discussions with Christof Löding while preparing a lecture on the Muller-Schupp algorithm.  ... 
doi:10.1016/j.tcs.2006.07.026 fatcat:pkgtelyqrbeuzch6flgt3bfpzm

Observations on Determinization of Büchi Automata [chapter]

Christoph Schulte Althoff, Wolfgang Thomas, Nico Wallmeier
2006 Lecture Notes in Computer Science  
The two determinization procedures of Safra and Muller-Schupp for Büchi automata are compared, based on an implementation in a program called OmegaDet.  ...  Acknowledgement We thank Detlef Kähler for his presentation of [14] in our seminar and remarks on a preliminary version of the paper; we relied on his work at several places.  ...  The second author acknowledges fruitful discussions with Christof Löding while preparing a lecture on the Muller-Schupp algorithm.  ... 
doi:10.1007/11605157_22 fatcat:tx5wbzzuqzcxvmjvh2fbdpqmhm

Omega Automata and its Classes

Natasha Singh, Ajay Kumar
2018 Current Science  
ω-automata is a variant of finite automata which accepts infinite strings.  ...  A variety of conditions are used to represent the set of accepting strings in ω-automata. This paper summarizes various types of ω-automata, their transition functions and accepting conditions.  ...  Identify the major applications of ω-automata Classification of papers After identifying the relevant papers, it was observed that ω-automata research papers can be categorized based on the research  ... 
doi:10.18520/cs/v115/i11/2042-2051 fatcat:byu5hbxpnbaclbp2rkx3qa6uhm

ω-Automata [article]

Thomas Wilke
2016 arXiv   pre-print
The main focus is on fundamental automata constructions, for instance, for boolean operations, determinization, disambiguation, and removing alternation.  ...  This paper gives a concise introduction into the basic theory of ω-automata (as of March 2014).  ...  A complementation construction for Büchi automata can now be based on Corollary 1(2) and the following observations.  ... 
arXiv:1609.03062v1 fatcat:tf7hsjxmkfdnnnzpjbbyg2c5lq

Good for Games Automata: From Nondeterminism to Alternation

Udi Boker, Karoliina Lehtinen, Michael Wagner
2019 International Conference on Concurrency Theory  
We then show that alternating GFG automata over finite words, and weak automata over infinite words, are not more succinct than deterministic automata, and that determinizing Büchi and co-Büchi alternating  ...  We leave open the question of whether alternating GFG automata of stronger acceptance conditions allow for doubly-exponential succinctness compared to deterministic automata.  ...  In Section 6, we focus on weak, Büchi, and co-Büchi automata, and then view α as a subset of Q. Games. A finite Σ-arena is a finite Σ×{A, E}-labeled Kripke structure.  ... 
doi:10.4230/lipics.concur.2019.19 dblp:conf/concur/BokerL19 fatcat:w6nqhu5o2zcg3j3jcexgyi4s5y

Nondeterminism in the Presence of a Diverse or Unknown Future [chapter]

Udi Boker, Denis Kuperberg, Orna Kupferman, Michał Skrzypczak
2013 Lecture Notes in Computer Science  
We show that GFT=GFG⊃DBP, and describe a determinization construction for GFG automata.  ...  Hoping to retain some of the advantages of nondeterministic automata, researchers have studied restricted classes of nondeterministic automata.  ...  GFG Büchi and co-Büchi Automata are not DBP There is a strong intuition that a GFG NBW can be determinized by pruning: By definition, the choices of a GFG NBW are independent on the future.  ... 
doi:10.1007/978-3-642-39212-2_11 fatcat:dr6tzu5efzd7hkjajjfwqjxpme

A LTL Fragment for GR(1)-Synthesis

Andreas Morgenstern, Klaus Schneider
2011 Electronic Proceedings in Theoretical Computer Science  
To this end, manually written deterministic omega-automata having GR(1) conditions were used instead of the original LTL specifications.  ...  However, new ideas have recently renewed the interest in LTL synthesis: One major new contribution in this area is the recent work of Piterman et al. who showed how polynomial time synthesis can be achieved  ...  Another one is the observation that the negation of each formula that can be translated to a deterministic Büchi automaton can be translated to a non-deterministic co-Büchi automaton.  ... 
doi:10.4204/eptcs.50.3 fatcat:3rbl34fmgvbvrp5oy533p3rike

An Effective Decision Procedure for Linear Arithmetic with Integer and Real Variables [article]

Bernard Boigelot, Sebastien Jodogne, Pierre Wolper
2003 arXiv   pre-print
The contribution of this paper is to show, using topological arguments, that only a restricted class of automata on infinite words are necessary for handling real and integer linear arithmetic.  ...  Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this involves some difficult and delicate to implement algorithms.  ...  automata is simpler than anything proposed for determinizing or complementing Büchi automata.  ... 
arXiv:cs/0303019v1 fatcat:r2oia4nasjhw3dujucglipba5u

Safety and Co-safety Comparator Automata for Discounted-Sum Inclusion [chapter]

Suguman Bansal, Moshe Y. Vardi
2019 Lecture Notes in Computer Science  
Discounted-sum comparator automata, or DS-comparators in short, are Büchi automata that read two infinite sequences of weights synchronously and relate their discounted-sum.  ...  Motivated by the connections between discounted-sum and Büchi automata, this paper undertakes an investigation of language-theoretic properties of DS-comparators in order to mitigate the challenges of  ...  Verma for their valuable inputs on initial drafts of the paper. This work was partially supported by NSF Grant No. CCF-1704883.  ... 
doi:10.1007/978-3-030-25540-4_4 fatcat:indbedgfmfczheuya6grjecgdy

How Deterministic are Good-For-Games Automata? [article]

Udi Boker, Orna Kupferman, Michał Skrzypczak
2017 arXiv   pre-print
In particular, when Rabin or Streett GFG automata have equivalent Buchi or co-Buchi GFG automata, respectively, then such equivalent automata can be defined on a substructure of the original automata.  ...  This practical issue is of special interest in the context of games, where the Buchi and co-Buchi conditions admit memoryless strategies for both players.  ...  Moreover, the best known determinization construction of GFG Büchi automata is quadratic, whereas determinization of GFG co-Büchi automata has an exponential blow-up lower bound [6] .  ... 
arXiv:1710.04115v1 fatcat:y4ycowj7lvf7fjrmnxyz5zsnau

Minimisation of Deterministic Parity and Buchi Automata and Relative Minimisation of Deterministic Finite Automata [article]

Sven Schewe
2011 arXiv   pre-print
put on top of it.  ...  We argue that minimisation of finite automata, hyper-minimisation, relaxed minimisation, and the minimisation of deterministic Buchi (or Co-Buchi) automata are operations of increasing reduction power,  ...  (One is often not really interested in differences on words that one never observes.) It surely is the better starting point for minimising DBAs and DCAs.  ... 
arXiv:1007.1333v2 fatcat:bv64datkofffzgeiilypyi6n3u

An effective decision procedure for linear arithmetic over the integers and reals

Bernard Boigelot, Sébastien Jodogne, Pierre Wolper
2005 ACM Transactions on Computational Logic  
The contribution of this paper is to show, using topological arguments, that only a restricted class of automata on infinite words are necessary for handling real and integer linear arithmetic.  ...  Previous work has shown that this theory can be dealt with by using finite automata on infinite words, but this involves some difficult and delicate to implement algorithms.  ...  weak automata is simpler than anything proposed for determinizing or complementing Büchi automata.  ... 
doi:10.1145/1071596.1071601 fatcat:5awxkx5vbjabdaog7ytlq7moia

Backward deterministic and weak alternating ω-automata [article]

Sebastian Preugschat, Thomas Wilke
2017 arXiv   pre-print
We present a direct transformation of weak alternating ω-automata into equivalent backward deterministic ω-automata and show (1) how it can be used to obtain a transformation of non-deterministic Büchi  ...  fragment of the linear-time μ-calculus as an intermediate step; (2) is based on the straightforward translation of linear-time temporal logic into weak alternating ω-automata.  ...  deterministic ω-automata can be derived.  ... 
arXiv:1701.01971v1 fatcat:hpym6vgr4bbgzaotjovhnl4ofq

Automata vs Linear-Programming Discounted-Sum Inclusion [chapter]

Suguman Bansal, Swarat Chaudhuri, Moshe Y. Vardi
2018 Lecture Notes in Computer Science  
This is a nuanced picture that is much richer than the one obtained from the theoretical study alone.  ...  In this work, we conduct the first empirical study of quantitative inclusion for discounted-sum weighted automata (DS-inclusion, in short).  ...  This work was partially supported by NSF Grant No. 1704883, "Formal Analysis and Synthesis of Multiagent Systems with Incentives".  ... 
doi:10.1007/978-3-319-96142-2_9 fatcat:vxwvy2bgarbnfmjmyuf6febkda

Can Nondeterminism Help Complementation?

Yang Cai, Ting Zhang
2012 Electronic Proceedings in Theoretical Computer Science  
In the case of nondeterministic finite automata on finite words (NFA), complementation and determinization have the same state complexity, namely Theta(2^n) where n is the state size.  ...  Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature.  ...  Büchi automata on conventional alphabets of fixed size.  ... 
doi:10.4204/eptcs.96.5 fatcat:lhuw2lyr45ae5ih52wx4nni77u
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