Deciding the Value 1 Problem of Probabilistic Leaktight Automata
نویسندگان
چکیده
The value 1 problem is a decision problem for probabilistic automata over finite words: given a probabilistic automaton A, are there words accepted by A with probability arbitrarily close to 1? This problem was proved undecidable recently. We sharpen this result, showing that the undecidability holds even if the probabilistic automata have only one probabilistic transition. Our main contribution is to introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is shown decidable (and PSPACE-complete). We construct an algorithm based on the computation of a monoid abstracting the behaviors of the automaton, and rely on algebraic techniques developed by Simon for the correctness proof. The class of leaktight automata is decidable in PSPACE, subsumes all subclasses of probabilistic automata whose value 1 problem is known to be decidable (in particular deterministic automata), and is closed under two natural composition operators.
منابع مشابه
A Class of Probabilistic Automata with a Decidable Value 1 Problem
The value 1 problem is a decision problem for probabilistic automata on finite words: given a probabilistic automatonA, are there words accepted byA with probability arbitrarily close to 1? This problem was proved undecidable recently. We introduce a new class of probabilistic automata, called leaktight automata, for which the value 1 problem is decidable. The algorithm is based on the computat...
متن کاملStamina: Stabilisation Monoids in Automata Theory
We present Stamina, a tool solving three algorithmic problems in automata theory. First, compute the star height of a regular language, i.e. the minimal number of nested Kleene stars needed for expressing the language with a complement-free regular expression. Second, decide limitedness for regular cost functions. Third, decide whether a probabilistic leaktight automaton has value 1, i.e. wheth...
متن کاملProbabilistic Timed Automata with Clock-Dependent Probabilities
Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition probabilities can depend linearly on clock values. Clock-dependent probabilistic timed automata allow the modelling of a continuous relationship between time...
متن کاملDeciding Probabilistic Automata Weak Bisimulation in Polynomial Time
Deciding in an efficient way weak probabilistic bisimulation in the context of probabilistic automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation. This enables us to arrive at a polynomial time algorithm for deciding ...
متن کاملACME: Automata with Counters, Monoids and Equivalence
We present ACME, a tool implementing algebraic techniques to solve decision problems from automata theory. The core generic algorithm takes as input an automaton and computes its stabilization monoid, which is a generalization of its transition monoid. Using the stabilization monoid, one can solve many problems: determine whether a B-automaton (which is a special kind of automata with counters)...
متن کامل