Deciding KAT and Hoare Logic with Derivatives

Kleene algebra with tests (KAT) is an equational system for program verification, which is the combination of Boolean algebra (BA) and Kleene algebra (KA), the algebra of regular expressions. In particular, KAT subsumes the propositional fragment of Hoare logic (PHL) which is a formal system for the specification and verification of programs, and that is currently the base of most tools for checking program correctness. Both the equational theory of KAT and the encoding of PHL in KAT are known to be decidable. In this paper we present a new decision procedure for the equivalence of two KAT expressions based on the notion of partial derivatives. We also introduce the notion of derivative modulo particular sets of equations. With this we extend the previous procedure for deciding PHL. Some experimental results are also presented.Comment: In Proceedings GandALF 2012, arXiv:1210.202

Prisoner of America

I wanted to expose the fact that many understand that we do not live in a just world but they do nothing to fight against it either, which makes them part of the problem. It just shows that you can know something is wrong, but if you chose not to do anything about it, then you have sided with the oppressors

Master\u27s Project: An Ecological Assessment of Merck Forest & Farmland Center, Rupert, Vermont

Merck Forest & Farmland Center is a 3190-acre property in Rupert, VT. It is a non-profit organization dedicated to the education of sustainable land management and farming practices. The Board of Trustees of Merck Forest is considering placing a conservation easement on the property through the Vermont Land Trust. In order to inform the easement recommendations a site assessment is necessary. During the summer of 2014, I mapped the natural communities to discover any ecologically sensitive areas on the property. Following the guidelines set by the Vermont Natural Heritage Program, I determined the element occurrence of rarity for each natural community and provided recommendations on management for the property. Using the Vermont Center for Ecostudies’ bird monitoring plot data I estimated the value of Merck Forest for habitat availability and diversity. Using the criteria of habitat connectivity, landscape complexity, and resiliency, I assessed the current and potential ecological value of this parcel in a regional context. I recommend a conservation strategy that follows a nested approach of preservation or ‘no-touch’ management areas within a larger matrix of conserved, actively managed land

Opportunities for Language Learning - a guide for students and parents

The booklet contains an outline of the different options givinging specific examples and illustrative case studies. The Teachers' Notes which accompany the booklet give some ideas about how to use this resource to help communicate the message to Sixth Form students in the process of making their future study choices. You can download the pdf here or contact us at [email protected] to request hard copies

"How to..." guide to holding an animation workshop in school

Thinking of holding a language event at school but don’t know where to start? We have created "How to..." guides from our most popular events to help you replicate them back in school. Each guide contains a full description of how to run the event including essential considerations, some sample programmes and task lists to give you an idea of what needs to be done and how to plan out the day. We also have some workshop ideas and resources which can be adapted for use with any language. You may find some the activities can be adapted to deliver during class time rather than as a formal event - please feel free to use these guides as you wish

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD). The key idea consists in computing a bisimulation by exploring reachable pairs symbolically, so as to avoid redundancies. This idea can be combined with already existing optimisations, and we show in particular a nice integration with the disjoint sets forest data-structure from Hopcroft and Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an algebraic theory that can be used for verification in various domains ranging from compiler optimisation to network programming analysis. This theory is decidable by reduction to language equivalence of automata on guarded strings, a particular kind of automata that have exponentially large alphabets. We propose several methods allowing to construct symbolic automata out of KAT expressions, based either on Brzozowski's derivatives or standard automata constructions. All in all, this results in efficient algorithms for deciding equivalence of KAT expressions