Adapting Behaviors via Reactive Synthesis

Abstract

In the Adapter Design Pattern, a programmer implements a Target interface by constructing an Adapter that accesses an existing Adaptee code. In this work, we present a reactive synthesis interpretation to the adapter design pattern, wherein an algorithm takes an Adaptee and a Target transducers, and the aim is to synthesize an Adapter transducer that, when composed with the Adaptee, generates a behavior that is equivalent to the behavior of the Target. One use of such an algorithm is to synthesize controllers that achieve similar goals on different hardware platforms. While this problem can be solved with existing synthesis algorithms, current state-of-the-art tools fail to scale. To cope with the computational complexity of the problem, we introduce a special form of specification format, called Separated GR(k), which can be solved with a scalable synthesis algorithm but still allows for a large set of realistic specifications. We solve the realizability and the synthesis problems for Separated GR(k), and show how to exploit the separated nature of our specification to construct better algorithms, in terms of time complexity, than known algorithms for GR(k) synthesis. We then describe a tool, called SGR(k), that we have implemented based on the above approach and show, by experimental evaluation, how our tool outperforms current state-of-the-art tools on various benchmarks and test-cases.

Mimicking Behaviors in Separated Domains

“…We first note that the framework in (Amram et al, 2021) can be adapted to an infinitetrace variant of MBSD, with target mapping specifications of the form Φ = k l=1 ( n l i=1 ♦(ϕ l,i ) → m l j=1 ♦(ψ l,j )). The results in (Amram et al, 2021), which build heavily on domain separation, can be tailored to obtain a polynomial-time algorithm for (explicit) separated domains in combined complexity. In contrast, Theorem 4 in this paper shows that the finite variant is PSPACE-hard already for much simpler mappings.…”

“…Mimicking has been recently studied in Formal Methods (Amram, Bansal, Fried, Tabajara, Vardi, & Weiss, 2021). In (Amram et al, 2021), the notion of mimicking is specified…”

Mimicking Behaviors in Separated Domains

“…Mimicking has been recently studied in Formal Methods (Amram, Bansal, Fried, Tabajara, Vardi, & Weiss, 2021). There, the notion of mimicking is specified in separated GR(k) formulas, a strict fragment of ltl.…”

“…Moreover, doing synthesis in ltl requires more sophisticated algorithms, a fact that, together with the need to suitably handle the details introduced by encoding ltl f into ltl, may further complicate the identification of the sources of complexity. In this respect, it is worth observing that in (Amram et al, 2021) the problem is encoded as a single ltl formula, without distinguishing the two domains and the mimicking specification, thus no attempt is made to provide a fine computational complexity analysis with respect to the domains and the mimicking specification, considered separately, as we do in this work.…”

“…MBSD provides us with a more general framework, set for finite-traces, and a wider spectrum of mapping specifications. In addition, this work, as well as (Amram et al, 2021), focuses on linear-time specifications, as opposed to the branching-time underlying simulation in .…”