Conflict-Driven Conditional Termination

Abstract

Conflict-driven learning, which is essential to the performance of sat and smt solvers, consists of a procedure that searches for a model of a formula, and refutation procedure for proving that no model exists. This paper shows that conflict-driven learning can improve the precision of a termination analysis based on abstract interpretation. We encode non-termination as satisfiability in a monadic second-order logic and use abstract interpreters to reason about the satisfiability of this formula. Our search procedure combines decisions with reachability analysis to find potentially non-terminating executions and our refutation procedure uses a conditional termination analysis. Our implementation extends the set of conditional termination arguments discovered by an existing termination analyzer.

Termination of Triangular Integer Loops is Decidable

“…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.…”

Proving Termination Through Conditional Termination

“…A first technique combined constraint-based methods for finding potential ranking functions with quantifier elimination [15] to infer preconditions. More recently, policy iteration-based methods [34], backwards reasoning in the abstract interpretation framework [45] and an adaptation of conflict-driven learning from satisfiability solving [17] have been adapted to find conditions for termination. Our algorithm CondTerm differs in its relative simplicity (by delegating the majority of the work to a constraint solver), and our procedure Term could combine it with or replace it by other approaches.…”

Inference of ranking functions for proving temporal properties by abstract interpretation

“…These and additional examples are available from FuncTion web interface: http://www.di.ens.fr/~urban/FuncTion.html. We refer to [8,23] for more extensive experimental evaluations restricted to program termination.…”

“…The recurrence semantics of a skip instruction is defined analogously to its guarantee semantics (cf. Equation 23), except that it resets the value of the input ranking function f : E O for the environments that satisfy ϕ only when they already belong to its domain:…”