• Intuitionistic Logic +

Intuitionistic logic extended with the assumption that some symbols are decidable (classical) combines classical and intuitionistic features.

• Validity Checking in Propositional Logic

Yet another decision procedure for the most notorious NP-complete problem - validity of propositional formulas

• Beyond Constant Propagation

Traditional data flow analyses can be extended to collect information about program expressions. This enhanced analysis is executed by a fixpoint algorithm that incorporates a rule-based inference procedure.

• Recursive Data Types in Java

Recursive types are classes containing members of the same type. Java classes are introduced to support recursive types. These classes facilitate traversal and updates of objects of recursive types. These classes simplify comparing and printing objects of recursive types as well as creation of internal representations when parsing various languages. These classes also contain methods implementing pattern matching.

• Finite State Machine Specification and Generation in Java

Finite state machines are specified directly in Java. State machine transitions are extended with regular expressions of events and unions of source states. Also, a notation for specifying assembly of state machines is introduced. Components are generated from the state machine specifications with extended transitions, and applications are generated from the assembly specifications.

• Automation of Component Communication in Java

Communication adapters can be automatically generated for Java components. This solution takes advantage of component hierarchies. It applies to J2EE components as well.

Math undoubtedly stands out from other disciplines due to its exclusive spiritual nature. Here are some math pearls substantiating the above statement, and I am especially delighted with them:

The Church-Turing thesis     Gödel's Incompleteness Theorems     Recursively Undecidable     Cantor's Diagonal Method

All these links lead to Eric Weisstein's World of Mathematics. It is an excellent online mathematical encyclopedia - the best I know of so far - hosted by Wolfram Research. See my own contributions to this encyclopedia:

Axiom Schema     Birkhoff's Theorem     Church-Rosser Property     Church-Rosser Theorem     Confluence     Creative Set     Critical Pair     Cut Elimination     Equational Logic     Finitely Terminating     First-Order Predicate Calculus     Formal Language     General Recursive Function     Godel Number     Grammar     Ground Atom     Ground Clause     Ground Literal     Herbrand Base     Herbrand's Theorem     Herbrand Universe     Horn Clause     Interpretation     Intuitionistic Logic     Kleene's Recursion Theorem     Kleene's s-m-n Theorem     Knuth-Bendix Completion Algorithm     Konig's Lemma     Loewenheim-Skolem Theorem     Modus Ponens     Partial Evaluation     Prenex Normal Form     Productive Set     Propositional Calculus     Recursively Isomorphic     Recursive Set     Recursively Enumerable Set     Recursively Undecidable     Reducible     Reduction Order     Reduction System     Regular Expression     Resolution     Resolution Principle     Rice's Theorem     Sequent Calculus     Skolem Function     Skolem Standard Form     Strict Order     Term Rewriting System     Unification     Universal Algebra
 

Check out the ultimate guide to Foundations of Mathematics It is my collection of links to quality materials on the subject. Some principal researches in this area contributed to the creation of this guide as well - see acknowledgement on that page. This guide is organized as a book contents page and intended to be a reference for studying foundations of mathematics. My other reference materials devoted to mathematical logic are: a comprehensive collection of Logical Laws     Sequent Calculus Primer with multiple derivation examples

Also, my son's 'triangular page' contains necessary information about triangles for school students.

Visit the web site of St. Petersburg Mathematical Society of which I am a member.

• Source Code Downloads
• Finite State Machines

• Data Languages
• XML Transformation