We develop two general approaches to characterising the manipulation of quantum states by means probabilistic protocols constrained limitations some resource theory. First, we give a necessary condition for existence physical transformation between states, obtained using recently introduced monotone based on Hilbert projective metric. In all affine theories (e.g. coherence, asymmetry, imaginari...

Reduction Systems and Idea of Knuth-Bendix Completion Algorithm Grzegorz Bancerek Association of Mizar Users Białystok, Poland Summary. Educational content for abstract reduction systems concerning reduction, convertibility, normal forms, divergence and convergence, ChurchRosser property, term rewriting systems, and the idea of the Knuth-Bendix Completion Algorithm. The theory is based on [1].

We identify the algebraic structure of material histories generated by concurrent processes. Specifically, we extend existing categorical theories resource convertibility to capture interaction. Our formalism admits an intuitive graphical presentation via string diagrams for proarrow equipments. also consider certain induced categories transducers, which are independent interest due their unusu...