Advanced automata-based algorithms for program termination checking

Termination of Triangular Integer Loops is Decidable

“…13 by showing how to compute poly-exponential expressions q 1 and q 3 that are equivalent to p 1 = n i=1 i − 1 = 0 · 4 n−i · 2 · w and p 3 = n i=1 4 n−i · (−2), respectively. For p 1 , according to (7) we have…”

“…While triangular loops are a very restricted subclass of general integer programs, integer programs often contain such loops. Hence, tools for termination analysis of such programs (e.g., [5,6,7,8,10,11,12]) could benefit from integrating our decision procedure and applying it whenever a sub-program is an affine triangular loop.…”

“…Hence, extensions of this example to a dimension greater than 4 where the loop is still triangular are not covered by any of the previous results. 7 Our proof that termination is decidable for triangular loops proceeds in three steps. We first prove that termination of triangular loops is decidable iff termination of non-negative triangular loops (nnt-loops) is decidable, cf.…”

The Termination and Complexity Competition

“…For all of these programming languages, AProVE uses an approach to transform the original program into a simple back-end language (an integer transition system or a combination of ITSs and TRSs) and to prove termination of the resulting back-end system instead [47]. In contrast, the tool UltimateAutomizer [16] uses a generalization of program paths to Büchi Automata in order to remove terminating paths. VeryMax [12] is based on a framework which allows to combine conditional termination proofs obtained using Max-SMT solvers in order to generate an (unconditional) termination proof of the program.…”

ROLL 1.0: $$\omega $$ -Regular Language Learning Library

“…Both of them are built on top of the BAs learning algorithms. Experiments [23] have shown that the resulting automata produced by the learning-based complementation can be much smaller than those built by structure-based algorithms [7,9,19,21,25]. Therefore, the learning-based complementation is suitable to serve as a baseline for Büchi automata complementation researches.…”