Related papers: Linear Ranking for Linear Lasso Programs

We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…

Synthesizing ranking functions is a common technique for proving the termination of loops. A ranking function must be bounded and decrease by a specified amount with each iteration for all reachable program states. However, the set of…

We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…

We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of…

Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program…

While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…

The extension of classical imperative programs with real-valued random variables and random branching gives rise to probabilistic programs. The termination problem is one of the most fundamental liveness properties for such programs. The…

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…

Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…

We present a novel decision tree-based synthesis algorithm of ranking functions for verifying program termination. Our algorithm is integrated into the workflow of CounterExample Guided Inductive Synthesis (CEGIS). CEGIS is an iterative…

A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…

There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a…

The termination problem for affine programs over the integers was left open in\cite{Braverman}. For more that a decade, it has been considered and cited as a challenging open problem. To the best of our knowledge, we present here the most…

We consider feasibility of linear integer programs in the context of verification systems such as SMT solvers or theorem provers. Although satisfiability of linear integer programs is decidable, many state-of-the-art solvers neglect…

In this paper, we consider lasso problems with zero-sum constraint, commonly required for the analysis of compositional data in high-dimensional spaces. A novel algorithm is proposed to solve these problems, combining a tailored active-set…

We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general term-orderings (instead of level mappings), like it is done in transformational approaches to logic program…

Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis…

We present an algorithm for synthesizing program loops satisfying a given polynomial loop invariant. The class of loops we consider can be modeled by a system of algebraic recurrence equations with constant coefficients. We turn the task of…

We learn sensor trees from training data to minimize sensor acquisition costs during test time. Our system adaptively selects sensors at each stage if necessary to make a confident classification. We pose the problem as empirical risk…