Finite state evaluation of logical formulas : Jevons' approach (1870) and contemporary description

Abstract

In this paper, we describe a formal language for a class of logical expressions. We then present a Finite State Machine for recognition and evaluation of this language. The main interest of the language is its historical characteristic. This language invented by the British scholar W. Stanley JEVONS in 1865 is probably the earliest language in which expressions were evaluated by a Finite State Machine. The two outstanding contributions were the use of machinery to evaluate formulas and the evaluation of formulas with variables by several parallel evaluations with constants. The contribution of this paper is to present this ancient evaluation process in a contemporary framework, i.e. formal languages and finite state automata. The design of an evaluator is given in great detail.