Automated deduction - CADE-17: 17th International Conference by David A. McAllester

By David A. McAllester

This e-book constitutes the refereed lawsuits of the seventeenth overseas convention on automatic Deduction, CADE-17, held in Pittsburgh, Pennsylvania, united states, in June 2000. The 24 revised complete examine papers and 15 process descriptions provided have been conscientiously reviewed and chosen from fifty three paper submissions and 20 process description submissions. additionally incorporated are contributions equivalent to invited talks and tutorials. The approved papers disguise a number of themes regarding theorem proving and its functions akin to proof-carrying code, cryptographic protocol verification, version checking, cooperating determination strategies, application verification, and backbone.

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Extra resources for Automated deduction - CADE-17: 17th International Conference on Automated Deduction, Pittsburgh, PA, USA, June 17-20, 2000 : proceedings, Volume 17, Part 2000

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A row i is said to be maximized at qi0 when all its non-zero entries are either in ∗-restricted columns or are negative and are in +-restricted columns. One such row is s3 in the tableau (b). Since 36 George C. Necula and Peter Lee s1 and s2 are known to be positive and s3 is a negative-linear combination of them, it follows that s3 ≤ q30 = 0. On the other hand after processing the third assertion we know that s3 ≥ 0 which leads Simplex to decide that s3 is both +-restricted and maximized at 0, hence it must be equal to zero.

To solve this complication we must also be able to express every ∗-restricted column as a negative linear combination of restricted owners. Simplex uses the two functions mapRow and mapCol shown in Figure 4 to construct negative linear combinations for a maximized row or a ∗-restricted column. In Figure 4 the notation Φ denotes a map from expressions to negative rational factors. All integer numerals n are represented as the numeral 1 with coefficient n. We use ∅ to denote the empty map. The operation Φ(E) ←+ q updates the map Φ increasing the coefficient of E by q.

When a disequality assertion a = b along with its proof neqab is encountered we first check whether a and b are equivalent. If they are then we announce 34 George C. Necula and Peter Lee a Contradiction with the proof falsei(prfEq(a, b), neqab). Otherwise we just add {(a = b, neqab)} to the undoStack and we update the forbid sets of both a and b. Note that congruence closure is a convex decision procedure and thus, it does not need to create case splits. Also, as proven in [NO80] and [Nel81] for similar implementations, the congruence closure algorithm is a sound and complete decision procedure for E.

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