Synthesizing Self-stabilization through Superposition and Backtracking

Specification-Based Synthesis of Distributed Self-Stabilizing Protocols

“…However, in our method, if the SMT-solver declares "unsatisfiability", it means that no self-stabilizing algorithm that satisfies the given input constraints exists. A complete synthesis technique for self-stabilizing systems is introduced in [22]. The limitations of this work compared to ours is: (1) unlike the approach in [22], we do not need the explicit description of the set of legitimate states, and (2) the method in [22] needs the set of actions on the underlying variables in the legitimate states.…”

“…Recently, Faghih and Bonakdarpour [14] proposed a sound and complete method to synthesize finite-state self-stabilizing systems based on SMT-solving. However, the shortcoming of this work as well as the techniques in [4,10,22] is that an explicit description of LS is needed as an input to the synthesis algorithm. The problem is that developing a formal predicate for legitimate states is not at all a straightforward task.…”

On the Applications of Interactive Theorem Proving in Computational Sciences and Engineering

“…Most existing techniques for the design of self-stabilization rely on a 'manual design and after-the-fact verification' methods which are limited to specific heuristics. Automatic finite-state synthesizers do exist [13,15,16,17] but they are efficient only in small scopes given the complexity of adding convergence problem (i.e., small finite number of processes) [15,16]. This dissertation includes two parts.…”

“…First, we propose a hybrid method for the synthesis and verification of parameterized self-stabilizing protocols, under the concept of synthesize in small scale then generalize. The first step of this method is done by automatic synthesizer [15,16,17]. By contrast, the generalization step is done by means of interactive prototype verification system (PVS).…”

“…The proposed method includes a synthesis step and a theorem proving step. In [26,25,14,40] the authors enable the synthesis step where they take a non-stabilizing protocol and generate a selfstabilizing version thereof that is correct by construction up to a certain number of processes. This paper investigates the second step where we use the theorem prover PVS to prove (or disprove) the correctness of the synthesized protocol for an arbitrary number of processes; i.e., generalize the synthesized protocol.…”