A framework for the study of periodic behaviour of twoway deterministic finite automata (2DFA) is developed. Computations of 2DFAs are represented by a two-way analogue of transformation semigroups, every element of which describes the behaviour of a 2DFA on a certain string x. A subsemigroup generated by this element represents the behaviour on strings in x. The main contribution of this paper...

We examine the conjecture that no polynomial can upper bound the increase in the number of states when a one-way nondeterministic finite automaton (1nfa) is converted into an equivalent two-way deterministic finite automaton (2dfa). We study the problem of liveness, which admits 1nfas of polynomial size and is known to defy 2dfas of polynomial size if and only if the conjecture is true. We focu...

We describe three regular expression-based methods to characterize as a regular language the language defined by a two-way automaton. The construction methods yield relatively simple techniques to directly construct one-way automata that simulate the behavior of two-way automata. The approaches also offer conceptually uncomplicated alternative equivalence proofs of two-way automata and one-way ...

In [1] it was shown that there are very effective attacks leading to collisions for the hash function MD4 designed by R. Rivest [3]. A summary of the status of hash functions of the MD4-family with respect to collision-resistence can be found in [2] and [4]. However, attacking the one-wayness of a hash function is a much more demanding challenge, and in case of success it has much more devastat...