Counterexample Guided Inductive Synthesis Modulo Theories

Abstract

Abstract. Program synthesis is the mechanised construction of software. One of the main difficulties is the efficient exploration of the very large solution space, and tools often require a user-provided syntactic restriction of the search space. We propose a new approach to program synthesis that combines the strengths of a counterexample-guided inductive synthesizer with those of a theory solver, exploring the solution space more efficiently without relying on user guidance. We call this approach CEGIS(T ), where T is a first-order theory. In this paper, we focus on one particular challenge for program synthesizers, namely the generation of programs that require non-trivial constants. This is a fundamentally difficult task for state-of-the-art synthesizers. We present two exemplars, one based on Fourier-Motzkin (FM) variable elimination and one based on first-order satisfiability. We demonstrate the practical value of CEGIS(T ) by automatically synthesizing programs for a set of intricate benchmarks.

cvc4sy: Smart and Fast Term Enumeration for Syntax-Guided Synthesis

“…We evaluated the above techniques in CVC4SY on four benchmark sets: invariant synthesis benchmarks from the verification of Lustre [11] models; a set from work on synthesizing invertibility conditions for bit-vector operators [12] (IC-BV); a set of bit-vector invariant synthesis problems [2] (CegisT); and the SyGuS-COMP 2018 [1] benchmarks from five tracks: assorted problems (General), conditional linear arithmetic problems (CLIA), invariant synthesis problems (INV), and programming-by-examples problems [10] with a set over bit-vectors (PBE-BV) and another over strings (PBE-Str). We also considered separately the CrCi subset from General, which corresponds to cryptographic circuit synthesis.…”

Solving Program Sketches with Large Integer Values

“…In the second variant, we set cbits = {5, 6, 7}, but reduce the number of missing hole values to 4 (i.e., we provide part of the invariant). Each benchmark takes two random inputs and we consider the following input ranges { [1,50], [1,100]}. In total, we have 10 benchmarks for mannadiv.…”

“…We consider the following simplified variants of the problem: (i ) petter_0 computes 1≤i≤n 1 and requires a polynomial invariant of degree one, (ii ) petter_x computes 1≤i≤n x for a given input variable x and requires a polynomial invariant of degree two, (iii ) petter_1 computes 1≤i≤n i and requires a polynomial invariant of degree two, and (iv ) petter_10 computes 1≤i≤n i + 1 and requires a polynomial invariant of degree two. Each benchmark takes two random inputs and we consider the following input ranges { [1,10], [1,100], [1,1000]}. In total, we have 12 variants of petter, each run for values of cbits ∈ {5, 6, 7}-i.e., a total of 36 benchmarks.…”

Verification and Synthesis of Symmetric Uni-Rings for Leads-To Properties

“…The set of such states is formally specified as the state predicate ∀i ∈ Z N : (x i−1 + x i = 2). We can represent this protocol as a graph containing arcs (0, 2, 1), (1,1,2), and (2, 0, 1) as shown in Figure 1. For simplicity, we assume that protocols consist of self-disabling processes.…”

“…As a result, τ ′ would include arcs (0, 1) and (2, 1), but excludes (3, 1) because r(3, 1) holds (see Figure 14-(a)). Executing Step 8 would result in including arcs (3,2) and (1,1), resulting in tree τ ′′ (Figure 14-(b)). Steps 9, 10, 11: The remaining steps of the algorithm labels τ ′′ (Figure 14-(b)), which would result in the action graph in Figure 15.…”