On the Hierarchy Classes of Finite Ultrametric Automata
نویسندگان
چکیده
This paper explores the language classes that arise with respect to the head count of a finite ultrametric automaton. First we prove that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognized by any k-head non-deterministic finite automaton. Then we prove that in the two-way setting the class of languages recognized by ultrametric finite k-head automata is a proper subclass of the class of languages recognized by (k + 1)-head automata. Ultrametric finite automata are similar to probabilistic and quantum automata and have only just recently been introduced by Freivalds. We introduce ultrametric Turing machines and ultrametric multi-register machines to assist in proving the results.
منابع مشابه
Kaspars Balodis Unconventional Finite Automata and Algorithms Doctoral
In this thesis we investigate several unconventional models of finite automata and algorithms. We start with more conventional types of automata and prove differentiation results for the descriptional complexity classes of twoway probabilistic and alternating finite automata. Then we introduce ultrametric finite automata which use p-adic numbers as amplitudes describing the branching process of...
متن کاملState Complexity Advantages of Ultrametric Automata
Ultrametric automata have properties similar to the properties of probabilistic automata but the descriptional power of these types of automata can differ very much. In this paper, we compare ultrametric automata with deterministic, nondeterministic, probabilistic and alternating automata with various state complexities. We also show that two-way ultrametric automata can have a smaller state co...
متن کاملUltrametric Automata with One Head Versus Multihead Nondeterministic Automata
The idea of using p-adic numbers in Turing machines and finite automata to describe random branching of the process of computation was recently introduced. In the last two years some advantages of ultrametric algorithms for finite automata and Turing machines were explored. In this paper advantages of ultrametric automata with one head versus multihead deterministic and nondeterministic automat...
متن کاملUnconventional Finite Automata and Algorithms
We investigate several unconventional models of finite automata and algorithms. We show that two-way alternating automata can be smaller than fast bounded-error probabilistic automata. We introduce ultrametric finite automata which use p-adic numbers to describe the branching process of the computation. We examine the size complexity of all the abovementioned automata for the counting problem. ...
متن کاملExperiments in Complexity of Probabilistic and Ultrametric Automata
We try to compare the complexity of deterministic, nondeterministic, probabilistic and ultrametric finite automata for the same language. We do not claim to have final upper and lower bounds. Rather these results can be considered as experiments to find advantages of one type of automata versus another type.
متن کامل