scholarly journals User-friendly Support for Common Mathematical Concepts in a Lightweight Verifier

10.29007/p79n ◽  
2018 ◽  
Author(s):  
Andrei Lapets
Keyword(s):  
Data Structure ◽  
Formal Verification ◽  
Logical Inference ◽  
Inference Algorithm ◽  
Formal Reasoning ◽  
Mathematical Concepts ◽  
Concrete Syntax ◽  
Verification Tools ◽  
Verification Systems ◽  
User Friendly

Machine verification of formal arguments can only increase our confidence in the correctness of those arguments, but the costs of employing machine verification still outweigh the benefits for some common kinds of formal reasoning activities. As a result, usability is becoming increasingly important in the design of formal verification tools. We describe the ``aartifact" lightweight verification system, designed for processing formal arguments involving basic, ubiquitous mathematical concepts. The system is a prototype for investigating potential techniques for improving the usability of formal verification systems. It leverages techniques drawn both from existing work and from our own efforts. In addition to a parser for a familiar concrete syntax and a mechanism for automated syntax lookup, the system integrates (1) a basic logical inference algorithm, (2) a database of propositions governing common mathematical concepts, and (3) a data structure that computes congruence closures of relations found in this database. Together, these components allow the system to better accommodate the expectations of users interested in verifying typical formal arguments involving algebraic manipulations of numbers, sets, vectors, and related operators and predicates. We demonstrate the reasonable performance of this system on typical formal arguments and briefly discuss how the system's design contributes to its usability in two use cases.

scholarly journals Guidelines for Formal Verification Systems

1989 ◽  
Author(s):  
Barbara A. Mayer ◽  
Monica M. Lu
Keyword(s):  
Formal Verification ◽  
Verification Systems

scholarly journals Fast equivalence -- checking for quantum circuits

2010 ◽  
Vol 10 (9&10) ◽  
pp. 721-734
Author(s):  
Shigeru Yamashita ◽  
Igor L. Markov
Keyword(s):  
Formal Verification ◽  
Quantum Algorithms ◽  
Quantum Circuits ◽  
Equivalence Checking ◽  
Sat Solvers ◽  
Reversible Circuits ◽  
Verification Tools ◽  
Verification Methodology ◽  
Verification Techniques ◽  
Factoring Algorithm

We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage existing techniques for simplification of quantum circuits. For reversible circuits which arise as runtime bottlenecks of key quantum algorithms, we develop several verification techniques and empirically compare them. We also combine existing quantum verification tools with the use of SAT-solvers. Experiments with circuits for Shor's number-factoring algorithm, containing thousands of gates, show improvements in efficiency by four orders of magnitude.

Dynamical Mathematical Software

2013 ◽  
pp. 70-88
Author(s):  
Samer Habre
Keyword(s):  
Learning Environment ◽  
Difference Equations ◽  
Mathematical Software ◽  
Mathematical Concepts ◽  
Visual Component ◽  
Innovative Methods ◽  
Modern Learning ◽  
Teaching Of Mathematics ◽  
User Friendly ◽  
The Way

Understanding mathematical concepts is many-folded. Traditional mathematics mostly emphasizes the algebraic/analytical aspect of a problem with minimal reference to its graphical aspect and/or numerical one. In a modern learning environment, however, multiple representations of concepts are proving to be essential for the teaching of mathematics. The availability of user-friendly dynamical software programs has paved the way for a radical yet smooth way for changing the way mathematical concepts are perceived. This chapter presents some of the author’s attempts for employing innovative methods in teaching topics in calculus, in differential and difference equations. The focus is on the use of dynamical programs that boost the visual component of the topics being investigated, hence contributing to a more complete understanding of these topics.

scholarly journals Dunuen: A User-Friendly Formal Verification Tool

2019 ◽  
Vol 159 ◽  
pp. 1431-1438
Author(s):  
Giovanni Capobianco ◽  
Umberto Di Giacomo ◽  
Francesco Mercaldo ◽  
Antonella Santone
Keyword(s):  
Formal Verification ◽  
Verification Tool ◽  
User Friendly

Making the NCTM Standards User Friendly for Child Care Teachers

2003 ◽  
Vol 9 (7) ◽  
pp. 421-427 ◽  
Author(s):  
Edith L. Skipper ◽  
Edna Neal Collins
Keyword(s):  
Early Childhood ◽  
Informal Learning ◽  
Formal Language ◽  
Learning Opportunities ◽  
Early Years ◽  
Early Childhood Curriculum ◽  
Nctm Standards ◽  
Mathematical Concepts ◽  
Everyday Activities ◽  
User Friendly

Principles and Standards for School Mathematics (NCTM 2000) asserts that mathematics is an essential part of the early childhood curriculum. The Standards encourage early childhood educators to nurture children's intuitive understandings of mathematical concepts by taking advantage of learning opportunities that naturally occur during everyday activities. In the context of these meaningful activities, learning can be increased by giving children the formal language with which to describe their informal learning (Clements and Sarama 2000), and young children's natural enthusiasm for mathematics can be nourished (Copley 2000). In particular, understanding of the concepts of number, geometry, and pattern is identified as essential in children's early years. Teachers also are encouraged to emphasize the processes involved in learning and doing mathematics, including problem solving, reasoning, communicating, connecting, and representing.

scholarly journals Modular specification and verification of closures in Rust

2021 ◽  
Vol 5 (OOPSLA) ◽  
pp. 1-29
Author(s):  
Fabian Wolff ◽  
Aurel Bílý ◽  
Christoph Matheja ◽  
Peter Müller ◽  
Alexander J. Summers
Keyword(s):  
Formal Verification ◽  
Functional Properties ◽  
Type System ◽  
Order Logic ◽  
First Order Logic ◽  
Formal Reasoning ◽  
First Order ◽  
Novel Technique ◽  
Smt Solvers ◽  
Specification And Verification

Closures are a language feature supported by many mainstream languages, combining the ability to package up references to code blocks with the possibility of capturing state from the environment of the closure's declaration. Closures are powerful, but complicate understanding and formal reasoning, especially when closure invocations may mutate objects reachable from the captured state or from closure arguments. This paper presents a novel technique for the modular specification and verification of closure-manipulating code in Rust. Our technique combines Rust's type system guarantees and novel specification features to enable formal verification of rich functional properties. It encodes higher-order concerns into a first-order logic, which enables automation via SMT solvers. Our technique is implemented as an extension of the deductive verifier Prusti, with which we have successfully verified many common idioms of closure usage.

Modeling security properties of authentication of cryptographic protocols using spin formal verification

2020 ◽  
pp. 21-25
Author(s):  
E.A. Perevyshina ◽  
L.K. Babenko
Keyword(s):  
Model Checking ◽  
Formal Verification ◽  
Temporal Logic ◽  
Cryptographic Protocols ◽  
Wide Range ◽  
Security Properties ◽  
Verification Tools ◽  
The Stability ◽  
Security Property ◽  
Ltl Model Checking

To assess the quality and security of cryptographic protocols, we use various formal verification tools, such as Scyther tool, Avispa, ProVerif. these formal verifiers can check the protocol for vulnerability to attacks on secrecy and authentication, as these are the most prevalent attacks on protocols. However, this is not enough to fully analyze the security of the protocol. In this article, we will use linear temporal logic (LTL) model checking with SPIN. This tool, unlike the formal verifiers listed above, is not designed for a specific application in the context of cryptographic protocols; however, it has a very wide range of possibilities. In particular, for each security property, it is possible to describe the behavior of an attacker and test for the stability of the protocol model to its various attacks. The purpose of this work is to describe the developed methodology for verifying the security of authentication properties using the SPIN verifier.

scholarly journals VeriAgent: an Approach to Integrating UML and Formal Verification Tools

2004 ◽  
Vol 95 ◽  
pp. 111-129 ◽  
Author(s):  
E. Mota ◽  
E. Clarke ◽  
A. Groce ◽  
W. Oliveira ◽  
M. Falcão ◽  
...  
Keyword(s):  
Formal Verification ◽  
Verification Tools

scholarly journals Language Supportive Teaching and Textbooks (LSTT) for Bilingual Classrooms Mathematics Teaching and Learning in Tanzania

2017 ◽  
Vol 6 ◽  
Author(s):  
Francis William ◽  
Jesse Ndabakurane
Keyword(s):  
Test Performance ◽  
Teaching And Learning ◽  
English Language ◽  
Mathematical Concepts ◽  
Mathematics Textbook ◽  
Qualitative Approaches ◽  
Data Collection And Analysis ◽  
Post Test ◽  
User Friendly ◽  
The Impact

The aim of this study was to assess the impact on teaching and learning using the LSTT (Language Supportive Teaching and Textbooks) project’s bilingual Mathematics textbook chapters among Form One students in selected rural community secondary schools in Tanzania. LSTT project was introduced in Tanzania in 2013 to enhance language supportive teaching among the disadvantaged rural groups identified as less competent in foreign languages. The study employed both quantitative and qualitative approaches in data collection and analysis.  It employed a bilingual approach whereby Kiswahili was used as a resource in learning mathematical concepts in English language. Its major findings indicated that the students’ post-test performance in Mathematics was higher in Dodoma and Lindi Regions compared to their pre-test performance.  The study concluded that having been oriented through LSTT textbook, the students were likely to start doing the exercises in the textbook without the facilitator’s or researcher’s support. Evidently, most of the students gained confidence and interest in Mathematics, having used the user friendly LSTT material.

Sign in / Sign up

Export Citation Format

Share Document