Two Recursively Inseparable Problems for Probabilistic Automata
نویسندگان
چکیده
This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not. A numberless probabilistic automaton can be instantiated into a probabilistic automaton by specifying the exact values of the non-zero probabilistic transitions. We show that the two following properties of numberless probabilistic automata are recursively inseparable: • all instances of the numberless automaton have value 1, • no instance of the numberless automaton has value 1.
منابع مشابه
Conjugacy of One-Dimensional One-Sided Cellular Automata is Undecidable
Two cellular automata are strongly conjugate if there exists a shiftcommuting conjugacy between them. We prove that the following two sets of pairs (F,G) of one-dimensional one-sided cellular automata over a full shift are recursively inseparable: (i) pairs where F has strictly larger topological entropy than G, and (ii) pairs that are strongly conjugate and have zero topological entropy. Becau...
متن کاملConcavely-Priced Probabilistic Timed Automata
Concavely-priced probabilistic timed automata, an extension of probabilistic timed automata, are introduced. In this paper we consider expected reachability, discounted, and average price problems for concavely-priced probabilistic timed automata for arbitrary initial states. We prove that these problems are EXPTIME-complete for probabilistic timed automata with two or more clocks and PTIME-com...
متن کاملComputing Laboratory CONCAVELY-PRICED PROBABILISTIC TIMED AUTOMATA
Concavely-priced probabilistic timed automata, an extension of probabilistic timed automata, are introduced. In this paper we consider expected reachability, discounted, and average price problems for concavely-priced probabilistic timed automata for arbitrary initial states. We prove that these problems are EXPTIME-complete for probabilistic timed automata with two or more clocks and PTIME-com...
متن کاملClassical Automata on Promise Problems
Promise problems were mainly studied in quantum automata theory. Here we focus on state complexity of classical automata for promise problems. First, it was known that there is a family of unary promise problems solvable by quantum automata by using a single qubit, but the number of states required by corresponding one-way deterministic automata cannot be bounded by a constant. For this family,...
متن کاملOn the construction of probabilistic diagnosers
This paper revisits the notions of observer and diagnoser, and adapts them to probabilistic automata, in a setting of weighted automata computations. In the non stochastic case, observers and diagnosers are obtained by standard elementary steps, as state augmentation, epsilon-reduction and determinization. It is shown that these steps can be adapted to probabilistic automata, and algorithms to ...
متن کامل