By Paritosh K Pandya, Jaikumar Radhakrishnan

ISBN-10: 3540206809

ISBN-13: 9783540206804

ISBN-10: 3540245979

ISBN-13: 9783540245971

This ebook constitutes the refereed court cases of the twenty third convention on Foundations of software program expertise and Theoretical desktop technological know-how, FST TCS 2003, held in Mumbai, India in December 2003. The 23 revised complete papers provided including four invited papers and the summary of an invited paper have been conscientiously reviewed and chosen from one hundred sixty submissions. A vast number of present themes from the idea of computing are addressed, starting from algorithmics and discrete arithmetic to logics and programming thought.

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**Example text**

Case We consider such that then As we have (due to condition 2c of a boundable monoid). We conclude with the induction hypothesis. A Separation Logic for Resource Distribution 31 Corollary 1. For any resource and any formula of the form iff for any such that is defined, Proof. Immediate consequence of Lemma 5 and condition 2 of Definition 9. As the case of the operator is the crux of the satisfaction problem, we have Theorem 1 (Satisfaction Decidability for BI). Given a boundable partial resource monoid for any BI formula and any resource is decidable.

The Diagonal Method 1. Let 2. 3. for all 4. ). 5. For let be the decomposition of Choose Theorem 2. The diagonal method yields connectors with edges. Proof: We have to show that condition (3) is satisfied. Consider By step 5 we have for some with Subtracting these relations we conclude and thus since gcd by the choice of This implies and so The claim follows by Lemma 1 using that and the fact that (by Bertrand’s theorem there is a prime between and see [9]). 18 A. Baltz‚ G. Jäger‚ and A. Srivastav Fig.

By induction on the structure of We develop some interesting cases. Case As and from condition 2a of a boundable monoid we deduce and Case By definition there exist and such that and Thus by lemma 4, there exist such that and By induction hypothesis, we can conclude. Case We consider such that then As we have (due to condition 2c of a boundable monoid). We conclude with the induction hypothesis. A Separation Logic for Resource Distribution 31 Corollary 1. For any resource and any formula of the form iff for any such that is defined, Proof.

### FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science by Paritosh K Pandya, Jaikumar Radhakrishnan

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