Related papers: Polytool: polynomial interpretations as a basis fo…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

Temporal Logic (TL) can be used to rigorously specify complex high-level specification for systems in many engineering applications. The translation between natural language (NL) and TL has been under-explored due to the lack of dataset and…

In the dependency pair framework for proving termination of rewriting systems, polynomial interpretations are used to transform dependency chains into bounded decreasing sequences of integers, and they play an important role for the success…

Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…

This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs.…

In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the…

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…

Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…

We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a…

A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be…

There are many techniques and tools to prove termination of C programs, but up to now these tools were not very powerful for fully automated termination proofs of programs whose termination depends on recursive data structures like lists.…

There are various kinds of type analysis of logic programs. These include for example inference of types that describe an over-approximation of the success set of a program, inference of well-typings, and abstractions based on given types.…

We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and…

Program specialization is a program transformation methodology which improves program efficiency by exploiting the information about the input data which are available at compile time. We show that current techniques for program…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

LP relaxation-based message passing algorithms provide an effective tool for MAP inference over Probabilistic Graphical Models. However, different LP relaxations often have different objective functions and variables of differing…

There are many techniques and tools for termination of C programs, but up to now they were not very powerful for termination proofs of programs whose termination depends on recursive data structures like lists. We present the first approach…

Propositional Linear Temporal Logic (LTL) is a popular formalism for specifying desirable requirements and security and privacy policies for software, networks, and systems. Yet expressing such requirements and policies in LTL remains…

Applying dynamic logics to program verifications is a challenge, because their axiomatic rules for regular expressions can be difficult to be adapted to different program models. We present a novel dynamic logic, called DLp, which supports…

We introduce a modified version of the well-known dependency pair framework that is suitable for the termination analysis of rewriting under forbidden pattern restrictions. By attaching contexts to dependency pairs that represent the…