Kleene Algebra
نویسندگان
چکیده
3 Dioids 4 3.1 Join Semilattices . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Join Semilattices with an Additive Unit . . . . . . . . . . . . 5 3.3 Near Semirings . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Variants of Dioids . . . . . . . . . . . . . . . . . . . . . . . . 6 3.5 Families of Nearsemirings with a Multiplicative Unit . . . . . 8 3.6 Families of Nearsemirings with Additive Units . . . . . . . . . 8 3.7 Duality by Opposition . . . . . . . . . . . . . . . . . . . . . . 9 3.8 Selective Near Semirings . . . . . . . . . . . . . . . . . . . . . 10
منابع مشابه
Kleene Algebra with Tests
Kleene algebras with tests provide a rigorous framework for equational speciication and veriication. They have been used successfully in basic safety analysis, source-to-source program transformation, and concurrency control. We prove the completeness of the equational theory of Kleene algebra with tests and *-continuous Kleene algebra with tests over language-theoretic and relational models. W...
متن کاملOn Partially Additive Kleene Algebras
We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras. We relate partially additive Kleene algebras to existing algebraic structures, by exhibiting categorical connections with Kleene algebras, partially additiv...
متن کاملA coalgebraic approach to Kleene algebra with tests
Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. Since the known automata-theoretic presentation of Kleene algebra with tests does not lend itsel...
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Independence-friendly logic is a conservative extension of first-order logic that has the same expressive power as existential second-order logic. In her Ph.D. thesis, Dechesne introduces a variant of independence-friendly logic called IFG logic. We attempt to algebraize IFG logic in the same way that Boolean algebra is the algebra of propositional logic and cylindric algebra is the algebra of ...
متن کاملA Free Construction of Kleene Algebras with Tests
In this paper we define Kleene algebra with tests in a slightly more general way than Kozen’s definition. Then we give an explicit construction of the free Kleene algebra with tests generated by a pair of sets. Moreover we show that our free Kleene algebra with tests is isomorphic to Kozen and Smith’s Kleene algebra with tests if their construction available, that is, a generator of the Boolean...
متن کاملSome Applications of Kleene Algebra
We will treat some application by using Kleene algebra and its properties. First, We will find the shortest path which links two given vertices in a directed (finite) graph. Also, we will give an algorithm to solve this problem by using the typed Kleene algebra. Finally, we use Kleene algebra to put any program in while free form.
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ورودعنوان ژورنال:
- Archive of Formal Proofs
دوره 2013 شماره
صفحات -
تاریخ انتشار 2013