Download Computation, Logic, Games, and Quantum Foundations. The Many by Adam Brandenburger, H. Jerome Keisler (auth.), Bob Coecke, PDF

By Adam Brandenburger, H. Jerome Keisler (auth.), Bob Coecke, Luke Ong, Prakash Panangaden (eds.)

This Festschrift quantity, released in honor of Samson Abramsky, comprises contributions written through a few of his colleagues, former scholars, and neighbors. In occasion of the sixtieth birthday of Samson Abramsky, a convention used to be held in Oxford, united kingdom, in the course of could 28-30, 2010. The papers during this quantity characterize his manifold contributions to semantics, good judgment, video games, and quantum mechanics.

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Elsevier Publ. pdf 42. : Categorical formulation of finite-dimensional quantum algebras. Communications in Mathematical Physics 304(3), 765–796 (2011) 43. : Gruppentheorie. Friedrich Vieweg und Sohn (1931) The Algebra of Directed Acyclic Graphs Marcelo Fiore and Marco Devesas Campos Computer Laboratory University of Cambridge Abstract. We give an algebraic presentation of directed acyclic graph structure, introducing a symmetric monoidal equational theory whose free PROP we characterise as that of finite abstract dags with input/output interfaces.

For p, q ∈ Proj(A, are equivalent: ), the following (a) p and q commute; (b) p · q ∈ Proj(A, ); (c) p · q is the greatest lower bound of p and q in the partial order Proj(A, ). Proof. Unfold the definitions of Theorem 10. In general, every commutative monoid of idempotents is a meet-semilattice with respect to the order p ≤ q ⇐⇒ p · q = p, and if it is furthermore finite, then it is even a (complete) lattice. As shown in [14], in this case the notion of an idempotent can be generalised to arbitrary types A → B.

Classical quantum distributive nondistributive This translates as follows to the level of operator algebra. classical quantum commutative noncommutative Thus, the combination yields the following slogan. 16], and has been a guiding thought within the quantum structures research community. Categorical Quantum Mechanics More recently, drawing on modern developments in logic and computer science, and mainly a branch called type-theory, Abramsky and Coecke introduced a radically different approach to quantum structures that has gained prominence, which takes compositional structure as the starting point [1].

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