Bounded Synthesis of Reactive Programs

Most algorithms for the synthesis of reactive systems focus on the construction of finite-state machines rather than actual programs. This often leads to badly structured, unreadable code. In this paper, we present a bounded synthesis approach that automatically constructs, from a given specification in linear-time temporal logic (LTL), a program in Madhusudan's simple imperative language for reactive programs. We develop and compare two principal approaches for the reduction of the synthesis problem to a Boolean constraint satisfaction problem. The first reduction is based on a generalization of bounded synthesis to two-way alternating automata, the second reduction is based on a direct encoding of the program syntax in the constraint system. We report on preliminary experience with a prototype implementation, which indicates that the direct encoding outperforms the automata approach

Synchronous Counting and Computational Algorithm Design

Consider a complete communication network on $n$ nodes, each of which is a state machine. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are "odd" and which are "even". We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates $f$ Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states. This work consists of two parts. In the first part, we use computational techniques (often known as synthesis) to construct very compact deterministic algorithms for the first non-trivial case of $f = 1$. While no algorithm exists for $n < 4$, we show that as few as 3 states per node are sufficient for all values $n \ge 4$. Moreover, the problem cannot be solved with only 2 states per node for $n = 4$, but there is a 2-state solution for all values $n \ge 6$. In the second part, we develop and compare two different approaches for synthesising synchronous counting algorithms. Both approaches are based on casting the synthesis problem as a propositional satisfiability (SAT) problem and employing modern SAT-solvers. The difference lies in how to solve the SAT problem: either in a direct fashion, or incrementally within a counter-example guided abstraction refinement loop. Empirical results suggest that the former technique is more efficient if we want to synthesise time-optimal algorithms, while the latter technique discovers non-optimal algorithms more quickly.Comment: 35 pages, extended and revised versio