Timed Context-Free Temporal Logics

The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and context-free properties by ensuring decidability and tractability in the combined setting. To this end we introduce two real-time linear temporal logics for specifying quantitative timing context-free requirements in a pointwise semantics setting: Event-Clock Nested Temporal Logic (EC_NTL) and Nested Metric Temporal Logic (NMTL). The logic EC_NTL is an extension of both the logic CaRet (a context-free extension of standard LTL) and Event-Clock Temporal Logic (a tractable real-time logical framework related to the class of Event-Clock automata). We prove that satisfiability of EC_NTL and visibly model-checking of Visibly Pushdown Timed Automata (VPTA) against EC_NTL are decidable and EXPTIME-complete. The other proposed logic NMTL is a context-free extension of standard Metric Temporal Logic (MTL). It is well known that satisfiability of future MTL is undecidable when interpreted over infinite timed words but decidable over finite timed words. On the other hand, we show that by augmenting future MTL with future context-free temporal operators, the satisfiability problem turns out to be undecidable also for finite timed words. On the positive side, we devise a meaningful and decidable fragment of the logic NMTL which is expressively equivalent to EC_NTL and for which satisfiability and visibly model-checking of VPTA are EXPTIME-complete.Comment: In Proceedings GandALF 2018, arXiv:1809.02416. arXiv admin note: A technical report with full details is available at arXiv:1808.0427

Verifying Quantitative Temporal Properties of Procedural Programs

We address the problem of specifying and verifying quantitative properties of procedural programs. These properties typically involve constraints on the relative cumulated costs of executing various tasks (by invoking for instance some particular procedures) within the scope of the execution of some particular procedure. An example of such properties is "within the execution of each invocation of procedure P, the time spent in executing invocations of procedure Q is less than 20 % of the total execution time". We introduce specification formalisms, both automata-based and logic-based, for expressing such properties, and we study the links between these formalisms and their application in model-checking. On one side, we define Constrained Pushdown Systems (CPDS), an extension of pushdown systems with constraints, expressed in Presburger arithmetics, on the numbers of occurrences of each symbol in the alphabet within invocation intervals (subcomputations between matching pushes and pops), and on the other side, we introduce a higher level specification language that is a quantitative extension of CaRet (the Call-Return temporal logic) called QCaRet where nested quantitative constraints over procedure invocation intervals are expressible using Presburger arithmetics. Then, we investigate (1) the decidability of the reachability and repeated reachability problems for CPDS, and (2) the effective reduction of the model-checking problem of procedural programs (modeled as visibly pushdown systems) against QCaRet formulas to these problems on CPDS

The Larch Environment - Python programs as visual, interactive literature

The Larch Environment' is designed for the creation of programs that take the form of interactive technical literature. We introduce a novel approach to combined textual and visual programming by allowing visual, interactive objects to be embedded within textual source code, and segments of source code to be further embedded within those objects. We retain the strengths of text-based source code, while enabling visual programming where it is bene�cial. Additionally, embedded objects and code provide a simple object-oriented approach to extending the syntax of a language, in a similar fashion to LISP macros. We provide a rapid prototyping and experimentation environment in the form of an active document system which mixes rich text with executable source code. Larch is supported by a simple type coercion based presentation protocol that displays normal Java and Python objects in a visual, interactive form. The ability to freely combine objects and source code within one another allows for the construction of rich interactive documents and experimentation with novel programming language extensions

An Epistemicist Solution to Curry's Paradox

This paper targets a series of potential issues for the discussion of, and modal resolution to, the alethic paradoxes advanced by Scharp (2013). I aim, then, to provide a novel, epistemicist treatment to Curry's Paradox. The epistemicist solution that I advance enables the retention of both classical logic and the traditional rules for the alethic predicate: truth-elimination and truth-introduction

Mathematical Formula Recognition and Automatic Detection and Translation of Algorithmic Components into Stochastic Petri Nets in Scientific Documents

A great percentage of documents in scientific and engineering disciplines include mathematical formulas and/or algorithms. Exploring the mathematical formulas in the technical documents, we focused on the mathematical operations associations, their syntactical correctness, and the association of these components into attributed graphs and Stochastic Petri Nets (SPN). We also introduce a formal language to generate mathematical formulas and evaluate their syntactical correctness. The main contribution of this work focuses on the automatic segmentation of mathematical documents for the parsing and analysis of detected algorithmic components. To achieve this, we present a synergy of methods, such as string parsing according to mathematical rules, Formal Language Modeling, optical analysis of technical documents in forms of images, structural analysis of text in images, and graph and Stochastic Petri Net mapping. Finally, for the recognition of the algorithms, we enriched our rule based model with machine learning techniques to acquire better results

Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

Decision trees usefully represent sparse, high dimensional and noisy data. Having learned a function from this data, we may want to thereafter integrate the function into a larger decision-making problem, e.g., for picking the best chemical process catalyst. We study a large-scale, industrially-relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pre-trained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models, or they may wish to optimize a discrete model that particularly well-represents a data set. We develop several heuristic methods to find feasible solutions, and an exact, branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on concrete mixture design instance and a chemical catalysis industrial instance