A distributed system can be characterised by autonomously acting agents, where each agent executes its own program, uses shared resources and communicates with the others, but otherwise is totally oblivious to the behaviour of the other agents. In a distributed adaptive system agents may change their programs, and enter or leave the collection at any time thereby changing the behaviour of the overall system. This article first develops a language-independent axiomatic definition of distributed adaptive systems and then presents concurrent reflective Abstract State Machines (crASMs), an abstract machine model for their specification. It can be proven that any distributed adaptive system as stipulated by the axiomatisation can be step-by-step simulated by a crASM. Proofs about crASMs can be grounded in a multiple-step logic, which extends known complete one-step logics for deterministic and non-deterministic ASMs.
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