The simulation of deterministic pushdown automata defined over a one-letter alphabet by finite state automata is investigated from a descriptional complexity point of view. We show that each unary deterministic pushdown automaton of size s can be simulated by a deterministic finite automaton with a number of states that is exponential in s. We prove that this simulation is tight. Furthermore, i...

We show that for all n and α such that 1 ≤ n ≤ α ≤ 2 there is a minimal n-state nondeterministic finite automaton whose equivalent minimal deterministic automaton has exactly α states.

We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, ...

In this paper we deal with 1-way multihead finite automata, in which the symbol under only one head (called read head) controls its move and other heads cannot distinguish the input symbols, they can only distinguish the end-marker from the other input symbols and they are called the blind head. We call such automaton a partially blind multihead automaton. We prove that partially blind k + 1-he...

We investigate the power of (1-reversal) counter machines (finite automata with multiple counters, where each counter can ‘‘reverse’’ only once, i.e., once a counter decrements, it can no longer increment) and one-way multihead finite automata (finite automata with multiple one-way input heads) as a language acceptor. They can be non-deterministic as well as augmented with a pushdown stack. Fir...

We prove that minimizing finite automata is NP-hard for almost all classes of automata that extend the class of deterministic finite automata. More specifically, we show that minimization is NP-hard for all finite automata classes that subsume the class of δNFAs which accept strings of length at most three. Here, δNFAs are the finite automata that are unambiguous, allow at most one state q with...

This paper introduces NL, a learning algorithm for inferring non-deterministic finite-state automata using membership and equivalence queries. More specifically, residual finite-state automata (RFSA) are learned similar as in Angluin’s popular L algorithm, which however learns deterministic finite-state automata (DFA). As RFSA can be exponentially more succinct than DFA, RFSA are the preferable...

Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A. Ambainis and R. Freivalds that quantum finite automata with pure states can have an exponentially smaller number of states than deterministic finite automata recognizing the same language. There was an unpublished ‘‘folk th...