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In 1978 Sakoda and Sipser raised the question of the cost, in terms of size of representations, of the transformation of two-way and one-way nondeterministic automata into equivalent two-way deterministic automata. Despite all the ...

We consider online algorithms. Typically, the model is investigated with respect to the competitive ratio. In this paper, we explore two-way automata and one-way automata as models for online algorithms. We focus on quantum and ...

It is shown that a two-way deterministic finite automaton (2DFA) with n states over an alphabet $\Sigma$ can be transformed to an equivalent one-way automaton (1DFA) with $|\Sigma |·\mathcal{F}(n)+1$ states, where $\mathcal{F}(n)={max}_{k=0}^n{k}^{n-k+1}\le {(n+1)}^{n+1}/{(ln(n+1)·e^{1-o(1)})}^{n+1}$.

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A two-dimensional automaton operates on arrays of symbols. While a standard (four-way) two-dimensional automaton can move its input head in four directions, restricted two-dimensional automata are only permitted to move their input heads in three ...

The row projection (resp., column projection) of a given two-dimensional language L is the one-dimensional language consisting of first rows (resp., first columns) of all two-dimensional words in L. The operation of row projection has previously ...

We consider online algorithms. Typically the model is investigated with respect to competitive ratio. In this paper, we explore two-way automata as a model for online algorithms. We focus on quantum and classical online algorithms. We show that ...

We explore the theory of regular language representations in the constructive type theory of Coq. We cover various forms of automata (deterministic, nondeterministic, one-way, two-way), regular expressions, and the logic WS1S. We give translations ...

The paper investigates the effect of basic language-theoretic operations on the number of states in two-way deterministic finite automata (2DFAs). If m and n are the number of states in the 2DFAs recognizing the arguments of the following operations, ...

We prove that two-way transducers (both deterministic and non-deterministic) cannot compress normal numbers. To achieve this, we first show that it is possible to generalize compressibility from one-way transducers to two-way transducers. These results ...

The question of the state-size cost for simulation of two-way nondeterministic automata (2nfas) by two-way deterministic automata (2dfas) was raised in 1978 and, despite many attempts, it is still open. Subsequently, the problem was attacked by ...

The paper determines the number of states in two-way deterministic finite automata (2DFA) over a one-letter alphabet sufficient and in the worst case necessary to represent the results of basic language-theoretic operations on 2DFAs with a certain ...

We describe an explicit simulation of 2-way nondeterministic automata by 1-way alternating automata with quadratic blow-up. We first describe the construction for automata on finite words, and extend it to automata on infinite words.