Probabilistic automata

Rabin, Michael O.

doi:10.1016/s0019-9958(63)90290-0

Cited by 621 publications

(361 citation statements)

References 2 publications

Supporting

Mentioning

357

Contrasting

Unclassified

Order By: Relevance

“…Rabin's probabilistic automata [27] can be modelled as weighted T-automata over the semiring [0, ∞) under the standard arithmetic operations. As we mentioned in Example 3.4), finitary probability distributions form a monad, which allows for a slightly more elegant formalization: we take the finitary distribution monad as T and B = [0, 1].…”

Section: T-automata: Examplesmentioning

confidence: 99%

Towards a Coalgebraic Chomsky Hierarchy

Goncharov¹,

Milius²,

Silva³

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. The Chomsky hierarchy plays a prominent role in the foundations of theoretical computer science relating classes of formal languages of primary importance. In this paper we use recent developments on coalgebraic and monadbased semantics to obtain a generic notion of a T-automaton, where T is a monad, which allows the uniform study of various notions of machines (e.g. finite state machines, multi-stack machines, Turing machines, valence automata, weighted automata). We use the generalized powerset construction to define a generic (trace) semantics for T-automata, and we show by numerous examples that it correctly instantiates for some known classes of machines/languages captured by the Chomsky hierarchy. Moreover, our approach provides new generic techniques for studying expressivity power of various machine-based models.

show abstract

Section: T-automata: Examplesmentioning

confidence: 99%

Towards a Coalgebraic Chomsky Hierarchy

Goncharov¹,

Milius²,

Silva³

2014

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…These processes include the probabilistic automata in the sense of [20]. -Alternating processes: every state that enables a non-Dirac transition enables only that transition.…”

Section: The Nplts Modelmentioning

confidence: 99%

Group-by-Group Probabilistic Bisimilarities and Their Logical Characterizations

Bernardo

Nicola

Loreti

2014

Trustworthy Global Computing

View full text Add to dashboard Cite

Abstract. We provide two interpretations, over nondeterministic and probabilistic processes, of PML, the probabilistic version of HennessyMilner logic used by Larsen and Skou to characterize bisimilarity of probabilistic processes without internal nondeterminism. We also exhibit two new bisimulation-based equivalences, which are in full agreement with the two different interpretations of PML. The new equivalences are coarser than the bisimilarity for nondeterministic and probabilistic processes proposed by Segala and Lynch, which instead is in agreement with a version of Hennessy-Milner logic extended with an additional probabilistic operator interpreted over state distributions rather than over individual states. The modal logic characterizations provided for the new equivalences thus offer a uniform framework for reasoning on purely nondeterministic processes, reactive probabilistic processes, and nondeterministic and probabilistic processes.

show abstract

“…We consider classical probabilistic finite automata (PFA) [21,20]. A PFA over alphabet A is a tuple A = (Q, ι, Acc, P) where Q is the finite set of states, ι ∈ Q is the initial state, and Acc ⊆ Q is the set of final states.…”

Section: Probabilistic Automatamentioning

confidence: 99%

“…Alternatively, they may make a probabilistic decision depending on the input letter, like (reactive) probabilistic automata [20]. The latter go back to Rabin [21] and are an object of ongoing research considering decision problems such as emptiness, language equivalence [24,28,9,10,18], and the value 1 problem [17].…”

Section: Introductionmentioning

confidence: 99%

A Probabilistic Kleene Theorem

Bollig

Gastin

Monmege

et al. 2012

Automated Technology for Verification and Analysis

View full text Add to dashboard Cite

Abstract. We provide a Kleene Theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. We provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a star operator. We prove that probabilistic expressions and probabilistic automata are expressively equivalent. Our result actually extends to two-way probabilistic automata with pebbles and corresponding expressions.

show abstract

Probabilistic automata

Cited by 621 publications

References 2 publications

Towards a Coalgebraic Chomsky Hierarchy

Towards a Coalgebraic Chomsky Hierarchy

Group-by-Group Probabilistic Bisimilarities and Their Logical Characterizations

A Probabilistic Kleene Theorem

Contact Info

Product

Resources

About