Termination and non-termination specification inference

Abstract

Techniques for proving termination and non-termination of imperative programs are usually considered as orthogonal mechanisms. In this paper, we propose a novel mechanism that analyzes and proves both program termination and non-termination at the same time. We first introduce the concept of second-order termination constraints and accumulate a set of relational assumptions on them via a Hoare-style verification. We then solve these assumptions with case analysis to determine the (conditional) termination and nontermination scenarios expressed in some specification logic form. In contrast to current approaches, our technique can construct a summary of terminating and non-terminating behaviors for each method. This enables modularity and reuse for our termination and non-termination proving processes. We have tested our tool on sample programs from a recent termination competition, and compared favorably against state-of-the-art termination analyzers.

Termination of Triangular Integer Loops is Decidable

“…. We search for q 1 , q 2 , q 3 ∈ PE[w] that are equivalent to p 1 , p 2 , p 3 , i.e., q 1 + q 2 + q 3 is equivalent to (12). We only show how to compute q 2 .…”

Automatic cyclic termination proofs for recursive procedures in separation logic

“…Many of these are, like our system, built on top of Hoare-style program logics. Closest to our work in this respect is HIPTNT+ [23] which extends a Hoare-style separation logic system with temporal operators expressing termination and both possible and definite non-termination, and is able to infer such temporal predicates for procedural programs. Also like our work, HIPTNT+ requires pre-/postcondition annotations for heap-manipulating procedures, and requires arithmetic parameters to be incorporated into inductive predicates (reflecting e.g.…”

“…We evaluate our implementation on a number of examples taken from the Termination Problems Database [33], demonstrating that our implementation is competitive with other termination tools (e.g. AProVE [20] and HIPTNT+ [23]).…”

Proving Termination Through Conditional Termination

“…In particular, this means that a non-termination proof for the narrowed program is a nontermination proof for the original program, as only terminating computations have been discarded by the transformation. Further, our program transformation does not only add information to the entry transitions (as in [32]) but also to all transitions occurring in the component under analysis. This significantly improves the precision of our otherwise unchanged non-termination analysis (cf.…”

“…Thus, a termination prover has to segment the program state space according to its termination behavior, ignoring non-terminating but unreachable states. Recent advances in termination proving try to tackle this problem by abducing conditions for non-termination, and focusing the termination proof search on the remaining state space [25,32]. However, these techniques rely on relatively weak non-termination proving techniques.…”