A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Computing the Rabin Index of a Parity Automaton

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). ...

##
###
Parityizing Rabin and Streett

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*...

##
###
Generalised Rabin(1) synthesis
[article]

2010
*
arXiv
*
pre-print

We furthermore show that

arXiv:1003.1684v2
fatcat:fkmakgvdezaa3fonpd7imqg4gi
*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*. ...##
###
Weak alternating automata and tree automata emptiness

1998
*
Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98
*

Beyond

doi:10.1145/276698.276748
dblp:conf/stoc/KupfermanV98
fatcat:vidxxgruqnadnjsrkuypamejem
*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. ...##
###
On the Complexity of Parity Word Automata
[chapter]

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*. ...

##
###
Tighter Bounds for the Determinisation of Büchi Automata
[chapter]

2009
*
Lecture Notes in Computer Science
*

We can construct standard

doi:10.1007/978-3-642-00596-1_13
fatcat:lso7d57zzzcz7oe4zyt37qotom
*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*...##
###
Rabinizer 4: From LTL to Your Favourite Deterministic Automaton
[chapter]

2018
*
Lecture Notes in Computer Science
*

We present

doi:10.1007/978-3-319-96145-3_30
fatcat:kowgdythzrc7teuvv5csf7xbeq
*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. ...##
###
Fair Equivalence Relations
[chapter]

2003
*
Lecture Notes in Computer Science
*

This hierarchy lies between

doi:10.1007/978-3-540-39910-0_30
fatcat:6c7kpqyb2vbhlmpbm43jbvbf5i
*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 . ...##
###
Fair Equivalence Relations
[chapter]

2000
*
Lecture Notes in Computer Science
*

This hierarchy lies between

doi:10.1007/3-540-44450-5_12
fatcat:dabexamcufepljiawgjdbs6psm
*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 . ...##
###
Generalized Rabin(1) Synthesis with Applications to Robust System Synthesis
[chapter]

2011
*
Lecture Notes in Computer Science
*

In this paper, we introduce generalized

doi:10.1007/978-3-642-20398-5_9
fatcat:suxg3bowarh77au4bsm3lnamje
*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 ...##
###
From Nondeterministic Büchi and Streett Automata to Deterministic Parity Automata

2007
*
Logical Methods in Computer Science
*

In addition,

doi:10.2168/lmcs-3(3:5)2007
fatcat:psmm2ykaqfffrlvu4nsykc4mxm
*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*). ...##
###
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]

2021
*
arXiv
*
pre-print

We prove that

arXiv:2105.12009v3
fatcat:53zbdhisnnathi2f74kdv4ke5u
*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 . ...##
###
Deciding Nondeterministic Hierarchy of Deterministic Tree Automata

2005
*
Electronical Notes in Theoretical Computer Science
*

We show an algorithm which, for

doi:10.1016/j.entcs.2004.05.015
fatcat:ibltgknkdfgxxihbuxztmbqity
*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. ...##
###
Determinising Parity Automata
[chapter]

2014
*
Lecture Notes in Computer Science
*

As

doi:10.1007/978-3-662-44522-8_41
fatcat:ktevnyi4dzeynhsrerisjjznza
*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. ...
« Previous

*Showing results 1 — 15 out of 359 results*