We present a complete axiomatization of test algebra ( 24, 18, 29]), the two-sorted algebraic variant of Propositional Dynamic Logic (PDL, 21, 7]). The axiomatization consists of ...
We present a development of Universal Algebra inside Type Theory, formalized using the proof assistant Coq. We define the notion of a signature and of an algebra over a signature. ...
We study the problem of polynomial identity testing (PIT) for depth 2 arithmetic circuits over matrix algebra. We show that identity testing of depth 3 (ΣΠΣ) arithmetic circuit...
In this paper we consider languages of labelled N-free posets over countable and scattered linear orderings. We prove that a language of such posets is series-rational if and only ...
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least ...