Truly Concurrent Process Algebra with Localities

Truly Concurrent Process Algebra with Localities introduces localities into truly concurrent process algebras. Traditional parallelism often existed in distributed computing, as distributed systems are usually autonomous and local computers have been single-core, single-processor, and timed (timed computing is serial in nature). Today, due to the progress of hardware, multi-cores, multi-processors, and GPUs are now making the local computer truly parallel. Concurrent computing is an important means of addressing complexity in structuring software systems, with huge impacts in many areas of computing, including increased program throughput, high responsiveness to input and output, and program structure that is more appropriate to certain tasks. Distribution is an important aspect of concurrent systems and reflects in their semantics. The distributed semantics gives a measure of the degree of parallelism in concurrent systems and keeps track of the local semantics of components within the concurrent system. Static localities say that processes are equated if they are at the same location and have the same behaviors at each location, while dynamic localities say that locations are associated with actions rather than parallel components. The well-known process algebras, such as CCS, ACP and ? -calculus, capture the interleaving concurrency based on bisimilarity semantics. In this book, readers will be able to explore all aspects of localities in truly concurrent process algebras, such as Calculus for True Concurrency (CTC), which is a generalization of CCS for true concurrency, Algebra of Parallelism for True Concurrency (APTC), which is a generalization of ACP for true concurrency and ? Calculus for True Concurrency (?). Together, these approaches capture the so-called true concurrency based on truly concurrent bisimilarities, such as pomset bisimilarity, step bisimilarity, history-preserving (hp-) bisimilarity and hereditary history-preserving (hhp-) bisimilarity. Truly concurrent process algebras are generalizations of the corresponding traditional process algebras. This book provides readers with all aspects of algebraic theory for localities, including the basis of semantics, calculi for static localities, axiomatization for static localities, as well as calculi for dynamic localities, and axiomatization for dynamic localities.