We prove the injectivity of Frobenius endomorphism on $\mathsf {B}_{\operatorname {cris}}$, {B}_{\max }$ and {st}}$.

In the current paper, we present search plans which can guide pattern matching for advanced graph patterns with edge identities, containment constraints, type variables, negative application conditions, attribute conditions, and injectivity constraints. Based on a generic search graph representation, all search plan operations (e.g. checking the existence of an edge, or extending a matching can...

We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injec...