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Questions tagged [probabilistic-automata]

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Computational power of probabilistic automata

I am a bit confused about the proper role of probabilistic automata (PA) in the theory of computation. Informally, I can imagine they can accept more than finite automata (FA) as they, for instance, ...
Barney's user avatar
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Probabilistic Logic Programming vs Stochastic Logic Programming

I'm reading the paper DeepStochLog: Neural Stochastic Logic Programming. The authors differentiate between Probabilistic Logic Programming (PLP) and Stochastic Logic Programming (SLP), but I can't ...
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Epsilon-closure and DFA minimization algorithms for probabilistic NFA

Are there any algorithms performing e-closures and DFA minimizations for probabilistic Finite Automata? Given that probabilistic NFAs might have multiple accepting paths for generating equivalent ...
jackb's user avatar
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How can I find the PhD thesis of C.A. Ellis?

I've searched for this article all over the web but couldn't find it. can anyone help me? Ellis, C.A. 1969. Probabilistic languages and automata. Rept. no. 355. Dept. Comp. Sc. University of Illinois, ...
Kooranifar's user avatar
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1 answer
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Palindrome language and Finite Automata Machines [closed]

I'm a grad student in math. I'm unaware of available literature in theoretical computer science, so require suggestions for books. Here are the two topics I'm interested in exploring. 1) A complete ...
Muhammad Adeel's user avatar
10 votes
1 answer
431 views

Introduction to probabilistic automata

Where can I find an introduction to probabilistic automata and what they recognize (certain functions from words to $[0,1]$)? Is there a standard term for such functions which are recognized by ...
Prateek's user avatar
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WFSA over hyperreals

Are there any works where authors tried to define weighted finite state automata over hyperreals (or a similar object allowing for infinite and infinitesimal values) in an attempt to make automata ...
hr0nix's user avatar
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Vector representation of probabilistic automaton

Suppose we have $N$ states $q_i$, $0\leq i<N$ Suppose we have $N\times N$ probability matrix $p_{ij}$, $0\leq i<N$, $0\leq j<N$, And suppose a machine, which is being in state $q_i$ then ...
Suzan Cioc's user avatar
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3 answers
578 views

Simplification of weighted NFA

What options does one have for the simplification (meaning reduction in the number of states) of weighted NFA over the probability semiring? From my understanding one can determinize, and then ...
hr0nix's user avatar
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2 votes
0 answers
785 views

What is the relationship between the number of states in Quantum Finite Automata and the number of non-regular languages they can recognize?

It is has been shown that Quantum Finite Automata can recognize at least some non-regular languages. What is the relationship between the number of states in a qfa and the number of non-regular ...
David Drane's user avatar
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$\omega$-regular properties of a 2-state Markov Chain

Let $X$ be a Markov Chain on a state space $\{0,1\}$ with a transition matrix $$ P = \left( \begin{align} 1-p & &p \\ q & &1-q \end{align} \right) $$ with both $p,q \in (0,1)$ so in ...
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Behaviour of Labelled Markov Processes

Labelled Markov Processes (LMP) seem to be a generalization of Probabilistic Automata (PA) studied by Segala to the case of the general state space. Namely, any LMP is given by a be a finite set of ...
SBF's user avatar
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7 votes
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158 views

Size complexity of probabilistic two-way automata for a Boolean function

I'm interested in computing Boolean functions $f:\{0,1\}^n\rightarrow\{0,1\}$ with two-way finite automata and I will measure the complexity of a Boolean function by the number of states for the ...
kbkb's user avatar
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169 views

The regularity of Markov chains with a threshold

(This question has been asked on math.se, with no response.) I am studying Paz's "Introduction to Probabilistic Automata" and there is an exercise I cannot solve: Ex. 11, p. 170: Let $\Sigma = \{a\...
Michaël Cadilhac's user avatar
4 votes
1 answer
509 views

Probabilistic circuit complexity or size of probabilistic 2-way automata for Boolean functions

If we consider circuits with arbitrary binary logic gates one can prove by a counting argument that there exists a Boolean function on $n$ variables that require a circuit of size $ \Theta \left( 2^n/...
kbkb's user avatar
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10 votes
0 answers
164 views

A language outside the Boolean closure of stochastic languages

Stochastic languages, that is, those accepted by probabilistic automata, are known to not be closed under intersection, union, concatenation, and morphism, even on unary languages. I have two ...
Michaël Cadilhac's user avatar