Related papers: Loops under Strategies ... Continued

We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…

Determining whether a given program terminates is the quintessential undecidable problem. Algorithms for termination analysis are divided into two groups: (1) algorithms with strong behavioral guarantees that work in limited circumstances…

A recent goal in the Reinforcement Learning (RL) framework is to choose a sequence of actions or a policy to maximize the reward collected or minimize the regret incurred in a finite time horizon. For several RL problems in operation…

Dependency pairs are one of the most powerful techniques to analyze termination of term rewrite systems (TRSs) automatically. We adapt the dependency pair framework to the probabilistic setting in order to prove almost-sure innermost…

One of the obstacles in automatic program proving is to obtain suitable loop invariants. The invariant of a loop is a weakened form of its postcondition (the loop's goal, also known as its contract); the present work takes advantage of this…

This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…

In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…

This paper is an expository contribution reporting on published work. It focusses on an approach followed in the rewriting community to formalize the concept of strategy. Based on rewriting concepts, several definitions of strategy are…

We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…

Invariants are the predominant approach to verify the correctness of loops. As an alternative, loop contracts, which make explicit the premise and conclusion of the underlying induction proof, can sometimes capture correctness conditions…

Programs with multiphase control-flow are programs where the execution passes through several (possibly implicit) phases. Proving termination of such programs (or inferring corresponding runtime bounds) is often challenging since it…

The problem of determining whether or not any program terminates was shown to be undecidable by Turing, but recent advances in the area have allowed this information to be determined for a large class of programs. The classic method for…

We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…

A left-corner parsing algorithm with top-down filtering has been reported to show very efficient performance for unification-based systems. However, due to the nontermination of parsing with left-recursive grammars, top-down constraints…

Many programs allow the user to input data several times during its execution. If the program runs forever the user may input data infinitely often. A program terminates if it terminates no matter what the user does. We discuss various ways…

Deep learning-based recommendation has become a widely adopted technique in various online applications. Typically, a deployed model undergoes frequent re-training to capture users' dynamic behaviors from newly collected interaction logs.…

We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…

For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is…