Complexity Theory for Splicing Systems [chapter]

Remco Loos, Mitsunori Ogihara
Lecture Notes in Computer Science  
This paper proposes a notion of time complexity in splicing systems. The time complexity of a splicing system at length n is defined to be the smallest integer t such that all the words of the system having length n are produced within t rounds. For a function t from the set of natural numbers to itself, the class of languages with splicing system time complexity t (n) is denoted by SPLTIME[ f (n)]. This paper presents fundamental properties of SPLTIME and explores its relation to classes based
more » ... on standard computational models, both in terms of upper bounds and in terms of lower bounds. As to upper bounds, it is shown that for any function t (n)SPLTIME[t (n)] is included in 1-NSPACE[t (n)]; i.e., the class of languages accepted by a t (n)-space-bounded nondeterministic Turing machine with one-way input head. Expanding on this result, it is shown that 1-NSPACE[t (n)] is characterized in terms of splicing systems: it is the class of languages accepted by a t (n)-space uniform family of extended splicing systems having production time O(t (n)) with the additional property that each finite automaton appearing in the family of splicing systems has at most a constant number of states. As to lower bounds, it is shown that for all functions t (n) ≥ log n, all languages accepted by a pushdown automaton with maximal stack height t (|x|) for a word x are in SPLTIME[t (n)]. From this result, it follows that the regular languages are in SPLTIME[O(log n)] and that the context-free languages are in SPLTIME[O(n)].
doi:10.1007/978-3-540-73208-2_29 fatcat:csus5xf2erdtjogroc5oy3moke