Infinite-state automata are a new invention: they are automata that have an infinite number of states represented by words, transitions defined us- ing rewriting, and with sets of initial and final states. Infinite-state automata have gained recent interest due to a remarkable result by Morvan and Stirling, which shows that automata with transitions defined using rational rewriting precisely capture context-sensitive (NLINSPACE) languages. In this paper, we show that infinite automata defined using a form of multi-stack rewriting precisely defines double exponential time (more precisely, 2ETIME, the class of problems solvable in 2^2^O(n) time). The salient aspect of this characterization is that the automata have no ostensible limits on time nor space, and neither direction of containment with respect to 2ETIME is obvious. In this sense, the result captures the complex- ity class qualitatively, by restricting the power of rewriting.
An Infinite Automaton Characterization of Double Exponential Time
PARLATO G
2008-01-01
Abstract
Infinite-state automata are a new invention: they are automata that have an infinite number of states represented by words, transitions defined us- ing rewriting, and with sets of initial and final states. Infinite-state automata have gained recent interest due to a remarkable result by Morvan and Stirling, which shows that automata with transitions defined using rational rewriting precisely capture context-sensitive (NLINSPACE) languages. In this paper, we show that infinite automata defined using a form of multi-stack rewriting precisely defines double exponential time (more precisely, 2ETIME, the class of problems solvable in 2^2^O(n) time). The salient aspect of this characterization is that the automata have no ostensible limits on time nor space, and neither direction of containment with respect to 2ETIME is obvious. In this sense, the result captures the complex- ity class qualitatively, by restricting the power of rewriting.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
