The Boolean Formula Value Problem as Formal Language

Abstract

The Boolean formula value problem asks for the Boolean output value of a given input formula. We code it as a formal language $\ensuremath{{\cal D_+}}\subset\{a,b\}^*$. ${\cal D_+}$ is a nonregular, visibly pushdown language. We give automata for ${\cal D_+}$ which enable us to derive some of its syntactic equations. It is unknown whether the given list of equations is complete. Using these equations some algebraic properties of the syntactic monoid of ${\cal D_+}$ are sketched.