T0L Systems and Languages

We discuss a family of systems and languages (called TOL) which have originally arisen from the study of mathematical models for the development of some biological organisms. From a formal language theory point of view, a TOL system is a rewriting system where at each step of a derivation every symbol in a string is rewritten in a context-free way, but different rewriting steps may use different sets of production rules and the language consists of all strings derivable from the single fixed string (the axiom). The family of TOL languages (as well as its different subfamilies considered here) is not closed with respect to usually considered operations; it is “incomparable” with context-free languages, but it is contained in the family of context-free programmed languages. TOL languages form an infinite hierarchy with respect to “natural” complexity measures introduced in this paper.

[1]  G. Herman.  I. General description and the problem of universal computing ability , 1971 .

[2]  G. Herman.  Role of environment in developmental models. , 1970, Journal of theoretical biology.

[3]  G. Herman.  Computing ability of a developmental model for filamentous organisms. , 1969, Journal of theoretical biology.

[4]  A. Lindenmayer.  Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[5]  Grzegorz Rozenberg,et al.  On 0L-Languages , 1971, Inf. Control..

[6]  Jeffrey D. Ullman,et al.  Formal languages and their relation to automata , 1969, Addison-Wesley series in computer science and information processing.

[7]  Aristid Lindenmayer,et al.  Mathematical Models for Cellular Interactions in Development , 1968 .

[8]  Gabor T. Herman,et al.  Closure Properties of Some Families of Languages Associated with Biological Systems , 1974, Inf. Control..

[9]  Daniel J. Rosenkrantz,et al.  Programmed Grammars and Classes of Formal Languages , 1969, JACM.

[10]  A. Lindenmayer.  Developmental systems without cellular interactions, their languages and grammars. , 1971, Journal of theoretical biology.

[11]  I. P. McWhirter.  Substitution Expressions , 1971, J. Comput. Syst. Sci..

[12]  A. Lindenmayer,et al.  Thioguanine-dependent Light Sensitivity of Perithecial Initiation in Sordaria fimicola , 1969 .

[13]  Rohit Parikh,et al.  On Context-Free Languages , 1966, JACM.

[14]  Sheila A. Greibach.  Full AFLs and Nested Iterated Substitution , 1970, Inf. Control..