Unary Probabilistic and Quantum Automata on Promise Problems
نویسندگان
چکیده
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs.
منابع مشابه
Classical 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 کاملDecision problems on unary probabilistic and quantum automata
It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with Skolem’s and positivity problems. We also introduce the concept of linear recurrence automata in order to show the connection naturally. Then, we also g...
متن کاملOn the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata
We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {Lm} of cyclic languages, where Lm = {a | k ∈ N}. In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language Lm with isolated cut point on one-way probabilistic finite automata is p1 1 +p α2 2 + · · ·+ps s , wit...
متن کاملProbabilistic and Nondeterministic Unary Automata
We investigate unary regular languages and compare deterministic finite automata (DFA’s), nondeterministic finite automata (NFA’s) and probabilistic finite automata (PFA’s) with respect to their size. Given a unary PFA with n states and an -isolated cutpoint, we show that the minimal equivalent DFA has at most n 1 2 states in its cycle. This result is almost optimal, since for any α < 1 a famil...
متن کاملCommunication complexity of promise problems and their applications to finite automata
Equality and disjointness are two of the most studied problems in communication complexity. They have been studied for both classical and also quantum communication and for various models and modes of communication. Buhrman et al. [6] proved that the exact quantum communication complexity for a promise version of the equality problem is O(logn) while the classical deterministic communication co...
متن کامل