By Sam Buss (auth.), Krishnendu Chatterjee, Jirí Sgall (eds.)
ISBN-10: 3642403123
ISBN-13: 9783642403125
ISBN-10: 3642403131
ISBN-13: 9783642403132
This ebook constitutes the completely refereed convention court cases of the thirty eighth foreign Symposium on Mathematical Foundations of computing device technology, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The sixty seven revised complete papers offered including six invited talks have been conscientiously chosen from 191 submissions. subject matters lined comprise algorithmic video game conception, algorithmic studying concept, algorithms and knowledge constructions, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency idea, databases and knowledge-based structures, foundations of computing, common sense in machine technology, types of computation, semantics and verification of courses, and theoretical concerns in man made intelligence.
Read or Download Mathematical Foundations of Computer Science 2013: 38th International Symposium, MFCS 2013, Klosterneuburg, Austria, August 26-30, 2013. Proceedings PDF
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Extra resources for Mathematical Foundations of Computer Science 2013: 38th International Symposium, MFCS 2013, Klosterneuburg, Austria, August 26-30, 2013. Proceedings
Example text
The following is new, and probably useful in other contexts. Our proof is intuitionistic. The proof is similar to Proposition 1, or to Theorem 1 of [26], but we need a few easy additional arguments near the end of the proof. Theorem 1. Every μ-term whose function symbols are all -accessible is mpo accessible. In particular, if is well-founded, then mpo is well-founded on μterms. Proof. One might think that Theorem 1 is an easy consequence of Proposition 1: encode μx s ¤ s½ as the ordinary term μÔs, s½ Õ, and the variable x as xÔÕ, and extend the precedence appropriately.
A term t is ground if and only if fvÔtÕ À, where the set fvÔtÕ of free variables of t is defined m inductively by fvÔxÕ ØxÙ, fvÔf Ôs1 , . . , sm ÕÕ s ¤ s½ Õ i 1 fvÔsi Õ, fvÔμx ½ ÔfvÔsÕ ØxÙÕ fvÔs Õ. For instance, μx f ÔxÕ ¤ gÔaÕ is a ground μ-term. Again, we give ourselves a precedence on Σ. We extend the definition of by letting μx s ¤ s½ μx t ¤ t½ if and only if s t and s½ t½ , and x x for every variable x. (We make an abuse of notation here and silently assume a form of α-renaming. A more correct definition would be: μx s ¤ s½ μy t ¤ t½ iff sÖx : z × tÖy : z × and s½ t½ , for z a fresh variable.
Minimal patterns. A second application arises from characterization 4. Given an upward closed language L of elements in a wqo X, one can test whether x È L by just checking finitely many equalities x1 x, . . , xn x. Indeed, property 4 states that one can write L as Øx1 , . . , xn Ù. For example, this is how van der Meyden shows that fixed monadic queries to indefinite databases can be evaluated in linear time in the size of the database [44], where x, x1 , . . , xn are (encodings of models as) finite sequences of finite sets of logical atoms.
Mathematical Foundations of Computer Science 2013: 38th International Symposium, MFCS 2013, Klosterneuburg, Austria, August 26-30, 2013. Proceedings by Sam Buss (auth.), Krishnendu Chatterjee, Jirí Sgall (eds.)
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