27,332 research outputs found
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 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 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 . While no algorithm exists
for , we show that as few as 3 states per node are sufficient for all
values . Moreover, the problem cannot be solved with only 2 states per
node for , but there is a 2-state solution for all values .
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
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