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Computing the Rabin Index of a Parity Automaton

Olivier Carton, Ramón Maceiras
1999 RAIRO - Theoretical Informatics and Applications  
The algorithm that we give in the next section computes the Rabin index of the set recognized by a parity automaton.  ...  THE ALGORITHM In this section, we describe the algorithm which computes the Rabin index of a set recognized by a parity automaton A = (Q)A,E,qo y 7r).  ... 
doi:10.1051/ita:1999129 fatcat:tnxmzrnnz5cerokizdryuvcf5a

Parityizing Rabin and Streett

Udi Boker, Orna Kupferman, Avital Steinitz, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
Parityizing Rabin and Streett index of the automaton.  ...  Finally, we use the construction of the parity condition in the deterministic case in order to solve the problem of deciding whether a given Rabin or Streett automaton has an equivalent parity automaton  ...  Formally, if A is a deterministic automaton with n states and there is a Rabin condition α of index k and a Streett condition β of index l such that the language of A with α is equal to the language of  ... 
doi:10.4230/lipics.fsttcs.2010.412 dblp:conf/fsttcs/BokerKS10 fatcat:q7l5cyskhfhojfwofcorhoesf4

Generalised Rabin(1) synthesis [article]

Ruediger Ehlers
2010 arXiv   pre-print
We furthermore show that the results obtained are in some sense tight, i.e., that there does not exist a similar synthesis method for assumptions and specifications of higher Rabin index, unless P=NP.  ...  In particular, we describe an efficient method to synthesize systems from linear-time temporal logic specifications for which all assumptions and guarantees have a Rabin index of one.  ...  For Rabin automata, |F| is also called the Rabin index of the automaton.  ... 
arXiv:1003.1684v2 fatcat:fkmakgvdezaa3fonpd7imqg4gi

Weak alternating automata and tree automata emptiness

Orna Kupferman, Moshe Y. Vardi
1998 Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98  
Beyond the independent interest of such translations, they give rise to a simple algorithm for deciding the nonemptiness of nondeterministic parity and Rabin tree automata.  ...  In a weak automaton, the state space is partitioned into partially ordered sets, and the automaton can proceed from a certain set only to smaller sets.  ...  In [Rab69] , Rabin described a non-elementary procedure for checking the nonemptiness of a given Rabin automaton and showed that the problem is decidable.  ... 
doi:10.1145/276698.276748 dblp:conf/stoc/KupfermanV98 fatcat:vidxxgruqnadnjsrkuypamejem

On the Complexity of Parity Word Automata [chapter]

Valerie King, Orna Kupferman, Moshe Y. Vardi
2001 Lecture Notes in Computer Science  
A simple translation of a parity automaton to an equivalent Büchi automaton is quadratic: a parity automaton with n states, m transitions, and index k may result in a Büchi automaton of size O((n + m)k  ...  The best known algorithm for the nonemptiness problem of parity automata goes through Büchi automata, leading to a complexity of O((n + m)k).  ...  The number k appearing in a parity or Rabin condition is called the index of the automaton.  ... 
doi:10.1007/3-540-45315-6_18 fatcat:crzwzl2uz5dz3j3fprkp4hc4bq

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 principle mechanism intuitively uses a Rabin condition on the transitions; we show how to obtain an equivalent Rabin transition automaton with approximately (1.65 n) n states from a nondeterministic  ...  If we want the size of the Rabin automaton to be independent of the alphabet size, or if we want to construct a deterministic parity automaton because of the computational advantages attached to parity  ... 
doi:10.1007/978-3-642-00596-1_13 fatcat:lso7d57zzzcz7oe4zyt37qotom

Rabinizer 4: From LTL to Your Favourite Deterministic Automaton [chapter]

Jan Křetínský, Tobias Meggendorfer, Salomon Sickert, Christopher Ziegler
2018 Lecture Notes in Computer Science  
We present Rabinizer 4, a tool set for translating formulae of linear temporal logic to different types of deterministic ω-automata.  ...  Further, we provide a distribution of PRISM that links Rabinizer and offers model checking procedures for probabilistic systems that are not in the official PRISM distribution.  ...  index appearance record of [KMWW17] keeps track of a permutation (ordering) of Rabin pairs.  ... 
doi:10.1007/978-3-319-96145-3_30 fatcat:kowgdythzrc7teuvv5csf7xbeq

Fair Equivalence Relations [chapter]

Orna Kupferman, Nir Piterman, Moshe Y. Vardi
2003 Lecture Notes in Computer Science  
This hierarchy lies between the hierarchies of word and tree automata, and it collapses at Rabin conditions of index one, and Streett conditions of index two. § bisimulation [GL94], game-bisimulation [  ...  For the linear paradigm, it is known that the Büchi condition is sufficiently strong (that is, a fair system that uses Rabin or Streett fairness can be translated to an equivalent Büchi system).  ...  The number of sets in a parity fairness condition or of pairs in a Rabin or Streett fairness condition is the index of 6 .  ... 
doi:10.1007/978-3-540-39910-0_30 fatcat:6c7kpqyb2vbhlmpbm43jbvbf5i

Fair Equivalence Relations [chapter]

Orna Kupferman, Nir Piterman, Moshe Y. Vardi
2000 Lecture Notes in Computer Science  
This hierarchy lies between the hierarchies of word and tree automata, and it collapses at Rabin conditions of index one, and Streett conditions of index two. § bisimulation [GL94], game-bisimulation [  ...  For the linear paradigm, it is known that the Büchi condition is sufficiently strong (that is, a fair system that uses Rabin or Streett fairness can be translated to an equivalent Büchi system).  ...  The number of sets in a parity fairness condition or of pairs in a Rabin or Streett fairness condition is the index of 6 .  ... 
doi:10.1007/3-540-44450-5_12 fatcat:dabexamcufepljiawgjdbs6psm

Generalized Rabin(1) Synthesis with Applications to Robust System Synthesis [chapter]

Rüdiger Ehlers
2011 Lecture Notes in Computer Science  
In this paper, we introduce generalized Rabin(1) synthesis as a solution to this problem.  ...  Our approach inherits the good algorithmic properties of generalized reactivity(1) synthesis but extends it to also allow co-Büchi-type assumptions and guarantees, which makes it usable for the synthesis  ...  Acknowledgements: This work was supported by the German Research Foundation (DFG) within the program "Performance Guarantees for Computer Systems" and the Transregional Collaborative Research Center "Automatic  ... 
doi:10.1007/978-3-642-20398-5_9 fatcat:suxg3bowarh77au4bsm3lnamje

From Nondeterministic Büchi and Streett Automata to Deterministic Parity Automata

Nir Piterman, Wolfgang Thomas
2007 Logical Methods in Computer Science  
In addition, the parity acceptance conditions allows to use more efficient algorithms (when compared to handling Rabin or Streett acceptance conditions).  ...  Determinization is used in numerous applications, such as reasoning about tree automata, satisfiability of CTL*, and realizability and synthesis of logical specifications.  ...  A parity condition of index 2k can be written as a Rabin (or Streett) condition with k pairs (without modifying the structure of the automaton).  ... 
doi:10.2168/lmcs-3(3:5)2007 fatcat:psmm2ykaqfffrlvu4nsykc4mxm

Page 5207 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
) Computing the Rabin index of a parity automaton.  ...  Summary: “The Rabin index of a rational language of infinite words given by a parity automaton with n states is computable in time O(n?c) where c is the cardinality of the alphabet.  ... 

On the Minimisation of Transition-Based Rabin Automata and the Chromatic Memory Requirements of Muller Conditions [article]

Antonio Casares
2021 arXiv   pre-print
We prove that the minimal amount of chromatic memory required in games using a given Muller condition is exactly the size of a minimal Rabin automaton recognising this condition.  ...  Our first contribution is a proof of the NP-completeness of the minimisation of transition-based Rabin automata.  ...  We first remark that by Theorem 28, the size of a minimal arena-independent memory for F coincides with the size of a minimal Rabin automaton for L F .  ... 
arXiv:2105.12009v3 fatcat:53zbdhisnnathi2f74kdv4ke5u

Deciding Nondeterministic Hierarchy of Deterministic Tree Automata

Damian Niwiński, Igor Walukiewicz
2005 Electronical Notes in Theoretical Computer Science  
We show an algorithm which, for a given deterministic parity automaton on infinite trees, computes the minimal Mostowski (or Rabin) index of a nondeterministic automaton recognizing the same language.  ...  This extends a previous result of Urbański on deciding if a given deterministic Rabin automaton is equivalent to a nondeterministic Büchi automaton.  ...  In the present paper we extend this result by showing an algorithm which, for a given deterministic parity automaton, computes its exact Mostowski index in the nondeterministic hierarchy.  ... 
doi:10.1016/j.entcs.2004.05.015 fatcat:ibltgknkdfgxxihbuxztmbqity

Determinising Parity Automata [chapter]

Sven Schewe, Thomas Varghese
2014 Lecture Notes in Computer Science  
As a side-result, this optimality extends to the determinisation of B\"uchi automata.  ...  We prove that the intermediate determinisation to Rabin automata is optimal. We show that the resulting determinisation to parity automata is optimal up to a small constant.  ...  with the parity index on the transitions from the states of the automata.  ... 
doi:10.1007/978-3-662-44522-8_41 fatcat:ktevnyi4dzeynhsrerisjjznza
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