math-PVS: A Large Language Model Framework to Map Scientific Publications to PVS Theories

As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in formalizing mathematics, and discovering connections between different mathematical areas, to name a few. While prior work has leveraged computers for exhaustive mathematical proof search, recent efforts based on large language models (LLMs) aspire to position computing platforms as co-contributors in the mathematical research process. Despite their current limitations in logic and mathematical tasks, there is growing interest in melding theorem proving systems with foundation models. This work investigates the applicability of LLMs in formalizing advanced mathematical concepts and proposes a framework that can critically review and check mathematical reasoning in research papers. Given the noted reasoning shortcomings of LLMs, our approach synergizes the capabilities of proof assistants, specifically PVS, with LLMs, enabling a bridge between textual descriptions in academic papers and formal specifications in PVS. By harnessing the PVS environment, coupled with data ingestion and conversion mechanisms, we envision an automated process, called \emph{math-PVS}, to extract and formalize mathematical theorems from research papers, offering an innovative tool for academic review and discovery

Effect of Piezoelectric Filed on the Optical Properties of (311) A and (311) B Oriented InAlAs/InP Heterostructures

InAlAs alloy was grown by MOCVD on an InP (311) substrate with different polarities. Measurements of photoluminescence (PL) and photoreflectance (PR) were performed to study the impact of the V/III flux ratio. It is discovered that the PL line was shifted to a greater energy side with the increasing excitation power density, and no saturation was observed of its related PL intensity. It is a fingerprint of type II transition emission. However, the recombination of the type II interface showed a powerful dependence on AsH3 overpressure and substrate polarity. In fact, we have noted an opposite behavior of type II energy transition shift from A to B polarity substrate in respect to V/III ratio variation. PR signals corresponding to Franz-Keldysh Oscillation (FKO) were observed. The analysis of their period has allowed one to assess the value of the PZ field in the samples. PL-luminescence measurements were performed out as a function of temperature. PL peak energy, PL intensity, and half maximum full width show anomalous behaviors. Indicating the existence of localized carriers, they were ascribed to the energy potential modulation associated with the indium cluster formation and PZ field

Powerful Techniques for the Automatic Generation of Invariants

. When proving invariance properties of programs one is faced with two problems. The first problem is related to the necessity of proving tautologies of the considered assertion language, whereas the second manifests in the need of finding sufficiently strong invariants. This paper focuses on the second problem and describes techniques for the automatic generation of invariants. The first set of these techniques is applicable on sequential transition systems and allows to derive so-called local invariants, i.e. predicates which are invariant at some control location. The second is applicable on networks of transition systems and allows to combine local invariants of the sequential components to obtain local invariants of the global systems. Furthermore, a refined strengthening technique is presented that allows to avoid the problem of size-increase of the considered predicates which is the main drawback of the usual strengthening technique. The proposed techniques are illustrated by ex..

Construction of abstract state graphs with PVS

We describe in this paper a method based on abstract interpretation which, from a theoretical point of view, is similar to the splitting methods proposed in [DGG93, Dam96] but the weaker abstract transition relation we use, allows us to construct automatically abstract state graphs paying a reasonable price. We consider a particular set of abstract states: the set of the monomials on a set of state predicates ' 1 ; :::; ' ` . The successor of an abstract state m for a transition ø of the program is the least monomial satisfied by all successors via ø of concrete states satisfying m. This successor m 0 can be determined exactly if for each predicate ' i it can be determined if ' i or :' i is a postcondition of m for ø . In order to do this, we use the Pvs theorem prover [SOR93] and our Pvs-interface defined in [GS96]. If the tactic used for the proof of the verification conditions is not powerful enough, only an upper approximation of the abstract successor m is constructed. This a..

Slicing SAL

Model checking has been successfully applied to verify nite-state systems albeit ones with small state-space. But most interesting systems have very large or in nite state-spaces. Automatic Abstraction techniques can help alleviate the state-space explosion problem to some extent. Another complementary approach is the use of program slicing to automatically remove portions of the input transition system irrelevant to the property being veri ed. This may result in state-space reduction. The reduced state system, if nite, may then be more amenable to model checking

Synthesizing Self-Contained Scientific Software - 2018 - Lightning Talk

Tool to build self-contained software packages