Synthesis of Large Dynamic Concurrent Programs from Dynamic Specifications

TL;DR

This paper introduces a scalable method for synthesizing large, dynamic concurrent programs that can grow at runtime, using automata-theoretic techniques to ensure correctness without state explosion.

Contribution

It presents a novel, efficient synthesis approach for dynamic concurrent programs that avoids state explosion by constructing pairwise automata instead of a full product automaton.

Findings

Method is polynomial in the number of active processes.

Successfully synthesizes correct programs with dynamic process creation.

Ensures correctness properties are inherited in large, evolving programs.

Abstract

We present a tractable method for synthesizing arbitrarily large concurrent programs, for a shared memory model with common hardware-available primitives such as atomic registers, compare-and-swap, load-linked/store conditional, etc. The programs we synthesize are dynamic: new processes can be created and added at run-time, and so our programs are not finite-state, in general. Nevertheless, we successfully exploit automatic synthesis and model-checking methods based on propositional temporal logic. Our method is algorithmically efficient, with complexity polynomial in the number of component processes (of the program) that are ``alive'' at any time. Our method does not explicitly construct the automata-theoretic product of all processes that are alive, thereby avoiding \intr{state explosion}. Instead, for each pair of processes which interact, our method constructs an automata-theoretic product (\intr{pair-machine}) which embodies all the possible interactions of these two processes. From each pair-machine, we can synthesize a correct \intr{pair-program} which coordinates the two involved processes as needed. We allow such pair-programs to be added dynamically at run-time. They are then ``composed conjunctively'' with the currently alive pair-programs to re-synthesize the program as it results after addition of the new pair-program. We are thus able to add new behaviors, which result in new properties being satisfied, at run-time. We establish a ``large model'' theorem which shows that the synthesized large program inherits correctness properties from the pair-programs.