A Characterization of Distributed ASMs with Partial-Order Runs

To overcome the practical limitations of partial-order runs of ‘distributed ASMs’ (Abstract State Machines) proposed by Gurevich, we have defined a concept of concurrent runs of multi-agent ASMs and could show that concurrent ASMs capture a natural language-independent axiomatic definition of concurrent algorithms, thus generalising Gurevich’s seminal ‘Sequential ASM Thesis’ from sequential to concurrent algorithms. However, we remained intrigued by the fact that Blass and Gurevich used partial-order runs of distributed ASMs to explain runs of sequential recursive algorithms. We discovered that also the inverse simulation holds: for every distributed ASM with partial order runs, these runs can be described by runs of a sequential recursive algorithm. This surprising result clarifies the difference in expressivity between partial-order and concurrent runs.