The Phenomenon of Non-Recursive Trade-Offs

Abstract

957-973 fP Wortd Scientific ' v ' n www.worldscientIfic.com Communicated by L. Hie and D. WotschkeNon-recursive trade-offs between different representations of languages reveal a basic phenomenon. The gain in economy of description can be arbitrary. The purpose of this paper is to survey the main aspects and results regarding different representations of languages whose relative succinctness is not recursively bounded. Basic properties of descriptional systems and reasonable size measures are addressed, and the unified fundamental proof schemes emerging from the literature are presented. A comprehensive overview of results is given. Finally, some new results are shown. In particular, it is proved that between each two levels of the infinite one-way fc-head finite automata hierarchies there is a non-recursive trade-off. Moreover, non-recursive trade-offs are shown between nondeterministic 2-head and deterministic fc-head automata. Keywords: Descriptional complexity; Non-recursive trade-offs; Size measures; Multihead finite automata. Int. J. Found. Comput. Sci. 2005.16:957-973. Downloaded from www.worldscientific.com by UNIVERSITY OF QUEENSLAND on 02/03/15. For personal use only.

Expressiveness and static analysis of extended conjunctive regular path queries

“…Kutrib [14]), we obtain a result on the relative succinctness of ECRPQs and CRPQs. One of the benefits of that technique is that it applies to a wide range of different reasonable definitions of the size of an ECRPQ.…”

Extended Regular Expressions: Succinctness and Decidability

“…Kutrib [19] provides more details on (and an extensive motivation of) complexity measures. Using this definition, we are able to define the notion of tradeoffs between classes of extended regular expressions: If no recursive upper bound for the tradeoff between RegEx(k) and RegEx(l) exists, we say that the tradeoff between RegEx(k) and RegEx(l) is non-recursive.…”

“…There is a considerable amount of literature on a wide range of non-recursive tradeoffs between various description mechanisms; for a survey, see Kutrib [19].…”

“…Kutrib [19]), we can use the fact that non-regularity is not semi-decidable to obtain a result on the relative succinctness of extended and proper regular expressions: (1) and CoFRegEx(0), using a complexity measure for RegEx(1).…”

“…Kutrib [19]). Thus, although the use of the "right" extended regular expression for a regular expression might offer arbitrary advantages in size (and, hence, parsing speed), these optimal expressions cannot be found effectively.…”