scholarly journals Bisimulations Meet PCTL Equivalences for Probabilistic Automata

2011 ◽  
pp. 108-123 ◽  
Author(s):  
Lei Song ◽  
Lijun Zhang ◽  
Jens Chr. Godskesen
Keyword(s):  
Probabilistic Automata

scholarly journals Lower bounds for the state complexity of probabilistic languages and the language of prime numbers

2020 ◽  
Vol 30 (1) ◽  
pp. 175-192
Author(s):  
NathanaËl Fijalkow
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Prime Numbers ◽  
Regular Languages ◽  
Automata Theory ◽  
Seminal Paper ◽  
Probabilistic Automata ◽  
State Complexity ◽  
Probabilistic Languages ◽  
Alternating Automata

Abstract This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. Motivated by the seminal paper of Rabin from 1963 introducing probabilistic automata, we study the (deterministic) state complexity of probabilistic languages and prove that probabilistic languages can have arbitrarily high deterministic state complexity. We then look at alternating automata as introduced by Chandra, Kozen and Stockmeyer: such machines run independent computations on the word and gather their answers through boolean combinations. We devise a lower bound technique relying on boundedly generated lattices of languages, and give two applications of this technique. The first is a hierarchy theorem, stating that there are languages of arbitrarily high polynomial alternating state complexity, and the second is a linear lower bound on the alternating state complexity of the prime numbers written in binary. This second result strengthens a result of Hartmanis and Shank from 1968, which implies an exponentially worse lower bound for the same model.

scholarly journals Bisimulations Meet PCTL Equivalences for Probabilistic Automata

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Lei Song ◽  
Lijun Zhang ◽  
Jens Godskesen ◽  
Flemming Nielson
Keyword(s):  
Probabilistic Automata

scholarly journals Probabilistic automata

1963 ◽  
Vol 6 (3) ◽  
pp. 230-245 ◽  
Author(s):  
Michael O. Rabin
Keyword(s):  
Probabilistic Automata

AN INVESTIGATION OF THE PHASE TRANSITIONS OF A FAMILY OF PROBABILISTIC AUTOMATA

2004 ◽  
Vol 07 (01) ◽  
pp. 93-123
Author(s):  
HEINZ MÜHLENBEIN ◽  
THOMAS AUS DER FÜNTEN
Keyword(s):  
Phase Transitions ◽  
Stationary Distribution ◽  
Classification Scheme ◽  
Mean Field ◽  
Finite Size ◽  
Order Parameters ◽  
Finite Size Scaling ◽  
Probabilistic Cellular Automata ◽  
Probabilistic Automata ◽  
Major Transitions

We investigate a family of totalistic probabilistic cellular automata (PCA) which depend on three parameters. For the uniform random neighborhood and for the symmetric 1D PCA the exact stationary distribution is computed for all finite n. This result is used to evaluate approximations (uni-variate and bi-variate marginals). It is proven that the uni-variate approximation (also called mean-field) is exact for the uniform random neighborhood PCA. The exact results and the approximations are used to investigate phase transitions. We compare the results of two order parameters, the uni-variate marginal and the normalized entropy. Sometimes different transitions are indicated by the Ehrenfest classification scheme. This result shows the limitations of using just one or two order parameters for detecting and classifying major transitions of the stationary distribution. Furthermore, finite size scaling is investigated. We show that extrapolations to n=∞ from numerical calculations of finite n can be misleading in difficult parameter regions. Here, exact analytical estimates are necessary.

Compositionality for Probabilistic Automata

2003 ◽  
pp. 208-221 ◽  
Author(s):  
Nancy Lynch ◽  
Roberto Segala ◽  
Frits Vaandrager
Keyword(s):  
Probabilistic Automata

Decidable and Expressive Classes of Probabilistic Automata

2015 ◽  
pp. 200-214 ◽  
Author(s):  
Rohit Chadha ◽  
A. Prasad Sistla ◽  
Mahesh Viswanathan ◽  
Yue Ben
Keyword(s):  
Probabilistic Automata
Sign in / Sign up

Export Citation Format

Share Document