Many different notions of "program property", and many different methods of verifying such properties, arise naturally in programming. We present a general framework of Specification Structures for combining different notions and methods in a coherent fashion. We then apply the idea of specification structures to concurrency in the setting of Interaction Categories. As a specific example, a certain specification

The compact closed bicategory Span of spans of reflexive graphs is described and it is interpreted as an algebra for constructing specifications of concurrent systems. We describe a procedure for associating to any Place/Transition system\Omega an expression \Psi\Omega in the algebra Span. The value of this expression is a system whose behaviours are the same as those of the P/T system. Furthermore, along the lines of Penrose's string diagrams, a geometry is associated to the expression \Psi\Omega which is essentially the same geometry as that usually associated to the net underlying \Omega .

In this paper I present a game model for the semantical analysis of handshake circuits. I show how the model captures effectively the composition of circuits in an associative way. Then I build a compact-closed category of handshake games and handshake strategies. I then consider the language Tangram and I define a semantics for this language simply by giving a denotation in the model to each handshake component that is used in the compilation of Tangram programs.

Traced monoidal categories of circuits are introduced in order to give a compositional account of circuits. Behaviour functors of circuits are dened, and compositionality results are obtained in terms of the structure-preserving properties of these functors. The theory includes models of the asynchronous binary circuits constructed from instantaneous functional circuits and upbounded inertial binary delays, as well as asynchronous pulse circuits such as pipelines. Via the notion of a circuit network, an explicit connection is made with the General Multiple-Winner circuit model.