Formal Languages as Models for Biological Growth

Abstract

A formal system is a mathematical structure S= (V, F, A, R), where (i). V is a set of symbols, called alphabet, V={a1 |i=0, 1, 2,...}. The set of all finite words (strings) composed with the elements of V is denoted by V*. Assuming the existence of an empty word Λ, the set V+ of nonempty words over V is then defined as V* -{Λ}. (ii). F⊂V* is a set of formulae, a language over V. (iii). A⊂F is a set of initial situations, called axioms. (iv). R is a set of rules of deduction (the primitives). A rule ρ∈R is defined as a subset of the Cartesian product Fn × F, where Fn is itself a Cartesian product F×...×F having n≥1 factors whose elements are the ordered n-tuples of formulae. Let F=(x1,..., xn) be an ordered n-tuple of formulae. If there exists a peR and a formula y such that Foy is obtained, then it is said that y is an immediate consequence of the premises (x1,..., xn). The formulae in F are the arguments of rule ρ. The set R of deduction rules defines the relation of immediate deducibility ( see Gross and Lentin, 1970). KeywordsFormal LanguageGenerative DeviceFinite AlphabetDeduction RuleFormal Language TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.