Boolean Functions: Topics in Asynchronicity

The essential guide showing how the unbounded delay model of computation of the Boolean functions may be used in the analysis of the Boolean networks

Boolean Functions: Topics in Asynchronicitycontains the most current research in several issues of asynchronous Boolean systems. In this framework, asynchronicity means that the functions which model the digital circuits from electronics iterate their coordinates independently on each other and the author—a noted expert in the field—includes a formal mathematical description of these systems.

Filled with helpful definitions and illustrative examples, the book covers a range of topics such as morphisms, antimorphisms, invariant sets, path connected sets, attractors. Further, it studies race freedom, called here the technical condition of proper operation, together with some of its generalized and strengthened versions, and also time reversal, borrowed from physics and also from dynamical systems, together with the symmetry that it generates.

This book:

• Presents up-to-date research in the field of Boolean networks,
• Includes the information needed to understand the construction of an asynchronous Boolean systems theory and contains proofs,
• Employs use of the language of algebraic topology and homological algebra.

Written formathematicians and computer scientists interested in the theory and applications of Boolean functions, dynamical systems, and circuits,Boolean Functions: Topics in Asynchronicityis an authoritative guide indicating a way of using the unbounded delay model of computation of the Boolean functions in the analysis of the Boolean networks.

Nyckelord: Guide to Boolean Functions; resource to Boolean functions; understanding Boolean functions; text on Boolean functions; The binary Boolean algebra; definition of the Boolean functions; examples of Boolean functions; Boolean functions stable and unstable coordinates; Modeling the asynchronous circuits; Sequences of sets and Boolean functions; predecessors and successors and Boolean functions; Functions that are compatible with the affine structure of Boolean functions; The Hamming distance Lipschitz functions; Affine spaces of successors and Boolean functions; A fixed point property and Boolean functions; Symmetrical functions relative to translations and Boolean functions; Antisymmetrical functions relative to translations; Antimorphisms vs predecessors and successors Homomorphic functions vs invariant sets