Read e-book online Computer Aided Verification: 17th International Conference, PDF

By George C. Necula, Sumit Gulwani (auth.), Kousha Etessami, Sriram K. Rajamani (eds.)

ISBN-10: 3540272313

ISBN-13: 9783540272311

ISBN-10: 3540316868

ISBN-13: 9783540316862

This quantity includes the lawsuits of the foreign convention on laptop Aided Veri?cation (CAV), held in Edinburgh, Scotland, July 6–10, 2005. CAV 2005 was once the 17th in a chain of meetings devoted to the development of the idea and perform of computer-assisted formal an- ysis equipment for software program and structures. The convention lined the spectrum from theoretical effects to concrete functions, with an emphasis on useful veri?cation instruments and the algorithms and methods which are wanted for his or her implementation. We obtained 123 submissions for normal papers and 32 submissions for software papers.Ofthesesubmissions,theProgramCommitteeselected32regularpapers and sixteen device papers, which shaped the technical software of the convention. The convention had 3 invited talks, via Bob Bentley (Intel), Bud Mishra (NYU), and George C. Necula (UC Berkeley). The convention was once preceded by way of an educational day, with tutorials: – computerized Abstraction Re?nement, through Thomas Ball (Microsoft) and Ken McMillan (Cadence); and – conception and perform of choice methods for combos of (First- Order) Theories, through Clark Barrett (NYU) and Cesare Tinelli (U Iowa). CAV 2005 had six a?liated workshops: – BMC 2005: third Int. Workshop on Bounded version Checking; – FATES 2005: fifth Workshop on Formal ways to trying out software program; – GDV 2005: 2d Workshop on video games in layout and Veri?cation; – PDPAR 2005: third Workshop on Pragmatics of determination tactics in - tomated Reasoning; – RV 2005: fifth Workshop on Runtime Veri?cation; and – SoftMC 2005: third Workshop on software program version Checking.

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Extra info for Computer Aided Verification: 17th International Conference, CAV 2005, Edinburgh, Scotland, UK, July 6-10, 2005. Proceedings

Example text

For a set of predicates P , a literal li over P is either a predicate pi or ¬pi , where pi ∈ P . A cube c over P is a conjunction of literals. A clause 2 We always use the term “predicate symbol” (and not “predicate”) to refer to symbols like “<”. Predicate Abstraction via Symbolic Decision Procedures 27 cl over P is a disjunction of literals. Finally, a minterm over P is a cube with |P | literals, and exactly one of pi or ¬pi is present in the cube. Given a set of predicates P = {p1 , . . , pn } and a formula e, the main operation in predicate abstraction involves constructing the weakest Boolean formula FP (e) over P such that FP (e) ⇒ e.

Initialization (a) W ← G ∪ E and W ← {}. (b) For each g ∈ G, t[(g, 0)] ← bg . (c) For each ei ∈ E, t[(¬ei , 0)] ← true. 2. For i = 1 to maxDerivDepth T (G ∪ E) do: (a) W ← W . (b) Initialize S(g) = {}, for any predicate g. (c) For every g ∈ W , S(g) ← S(g) ∪ {t[(g, i − 1)]}. (d) For every g, if (g : − g1 , . . , gk ) and gm ∈ W for all m ∈ [1, k]: i. Update the set of derivations of g at this level: ⎞ ⎛ t[(gm , i − 1)]⎠} S(g) ← S(g) ∪ {⎝ (2) m∈[1,k] ii. W ← W ∪ {g}. (e) For each g ∈ W : t[(g, i)] ← d∈S(g) d (f) For each g ∈ W , t[(g, )] ← t[(g, i)] 3.

Consider an example where G contains a set of predicates that denotes an “almost” fully connected graph over vertices x1 , . . , xn . G contains an equality predicate between every pair of variables except the edge between x1 . and xn . Let E = {x1 = xn }. After one iteration of the SDPT algorithm on this example, W will contain an equality between every pair of variables including x1 and xn since x1 = xn can be derived from x1 = xi , xi = xn , for every 1 < i < n. Therefore, if the SDPT algorithm terminates once the set of predicates in W terminates, the procedure will terminate after two steps.

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Computer Aided Verification: 17th International Conference, CAV 2005, Edinburgh, Scotland, UK, July 6-10, 2005. Proceedings by George C. Necula, Sumit Gulwani (auth.), Kousha Etessami, Sriram K. Rajamani (eds.)

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