The Mortality Threshold for Partially Monotonic Automata

Abstract

A deterministic incomplete automaton ${\mathcal A}=\langle Q,\Sigma,\delta\rangle$ is partially monotonic if its state set Q admits a linear order such that each partial transformation $\delta(\rule{6pt}{.4pt}\,,a)$ with a∈Σ preserves the restriction of the order to the domain of the transformation. We show that if ${\mathcal A}$ possesses a ‘killer’ word w∈Σ^* whose action is nowhere defined, then ${\mathcal A}$ is ‘killed’ by a word of length $|Q|+\left\lfloor\dfrac{|Q|-1}2\right\rfloor$.