On Regular Sets of Bounds and Determinism versus Nondeterminism

On determinism versus unambiquous nondeterminism for decision trees

Evolving algebras 1993: Lipari guide

2 Static Algebras and Updates 4 2.1 Static Algebras: Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Vocabularies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Definition of Static Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Regular Expressions with Counting: Weak versus Strong Determinism

We study deterministic regular expressions extended with the counting operator. There exist two notions of determinism, strong and weak determinism, which almost coincide for standard regular expressions. This, however, changes dramatically in the presence of counting. In particular, we show that weakly deterministic expressions with counting are exponentially more succinct and strictly more ex...

State Complexity of Nondeterministic Finite Automata with Limited Nondeterminism

Various approaches of quantifying nondeterminism in nondeterministic finite automata (NFA) are considered. We consider nondeterministic finite automata having finite tree width (ftw-NFA) where the computation on any input string has a constant number of branches. We give effective characterizations of ftw-NFAs and a tight bound for determinizing an ftw-NFA A as a function of the tree width and ...

Combinatorial Lower Bound Arguments for Deterministic and Nondeterministic Turing Machines

We introduce new techniques for proving quadratic lower bounds for deterministic and nondeterministic 1-tape Turing machines (all considered Turing machines have an additional one-way input tape). In particular, we derive for the simulation of 2-tape Turing machines by 1-tape Turing machines an optimal quadratic lower bound in the deterministic case and a nearly optimal lower bound in the nonde...