W. Pugh, and D. Wonnacott. Experience with Constraint-Based Array Dependence Analysis. Technical Report CS-TR-3371. University of Maryland (1994).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....We make this assumption nevertheless, for simplicity. provers is the Fourier Motzkin (FM) variable elimination method [2] which is used in popular tools like PVS [14] ICS [8] SVC [1] IMPS [7] and others. A variation of FM can also be used for solving QFP, as being done in the omega library [18]. We will describe in detail how this method works in section 2. Although FM has a worst case super exponential complexity, it is popular because it is frequently faster than competing methods for the size of instances encountered in practice. Hence, the current practice in solving both QFP and ....

....FM to handle a combination of strict ( and weak ( inequalities is simple. If either the lower or upper bound are a strict inequality, then so is the resulting constraint. Fourier Motzkin for integer variables An extension of Fourier Motzkin for eliminating integer variables was described in [17, 18] as part of the omega test . The omega test is quite complex and its full description is beyond the scope of this article. Below we summarize the core principles of this method. The important point is that like the original FM, eliminating an integer variable is done by deriving a new set of ....

[Article contains additional citation context not shown here]

W. Pugh and D. Wonnacott. Experiences with constraint-based array dependence analysis. In Principles and Practice of Constraint Programming, pages 312-325, 1994.

....applies for , and . Incorporating rules for those operators is therefore straightforward. For 6= things are a little bit more complicated, since it is not part of ILP. Although Omega test can handle negation, it is not desirable to keep it, since Omega test cannot deal with it very well [13]. Using the additive inverse 7 , it follows that [n] 6= 0 [n] iff [n] 1 [n] Therefore: a [n] 6= b [n] iff a [n] b [n] n] n] with [n] 1 [n] New variables ; are introduced and a [n] 6= b [n] is modeled as: a [n] 6= b [n] a = b 2 n with 1 2 n 1 1 3.4 ....

W. Pugh and D. Wonnacott. Experiences with constraintbased array dependence analysis. Technical report, University of Maryland, College Park, MD, 1994.

....methods is quite close, since transitive closure can be thought of as a cumulative form of projection with redundancy elimination. The SUPINF method [2, 20] is complete over the real numbers, but the class of integer constraints on which it is complete is not clearly defined. The Omega test [15, 16] and the algorithm of [10] adapt Fourier s projection algorithm for real numbers to integers. The former computes a disjunction of constraints, whereas the latter accumulates additional conditions that must be satisfied. All these algorithms have essentially theorem proving applications, and have ....

Pugh, W., Wonnacott, D.: Experiences with Constraint-based Array Dependence Analysis. Proc. Principles and Practice of Constraint Programming.PCP'94. 1994.

....as a conjunction of linear equalities and inequalities, the Omega test can be used to check whether P is a tautology, whether P is satisfiable, and whether P Q is a tautology. Checking whether P is a tautology is trivial. For more details on the Omega Library, see Kelly et al. [44] and Pugh et al. [67,68,69]. 6.3 Induction Iteration Method When the untrusted code contains loops, we need to synthesize loop invariants. In our system, the synthesis of loop invariants is attempted by means of the thesis.fm Page 83 Tuesday, December 19, 2000 11:00 AM 84 induction iteration method. We present the basic ....

W. Pugh, and D. Wonnacott. Experience with Constraint-Based Array Dependence Analysis. Technical Report CS-TR-3371. University of Maryland (1994).

....affine constraints on integer variables with the logical operations , and , and the quantifiers and . The affine constraints can be either equality or inequality constraints [10] Presburger formulas are decidable. For more details on the Omega Library, see Kelly et al. [10] and Pugh et al. [24,25,26]. When the untrusted code involves loops, an additional step is needed to synthesize loop invariants. In our system, the synthesis of loop invariants is attempted by means of the induction iteration method [35] We have extended the induction iteration method to synthesize loop invariants for ....

W. Pugh, and D. Wonnacott. Experience with Constraint-based Array Dependence Analysis. Technical Report CS-TR3371. University of Maryland. (1994).

.... poorly on moderate to large systems of constraints where the constraints are dense (each constraint involves many variables) However, the constraints I have seen in both dependence analysis and code generation are quite sparse, and Fourier elimination is quite efficient for sparse constraints [PW94a] Collard, Feautrier and Risset [CFR93] show how PIP, a parametrized version of the Dual Simplex Method, can be used to solve the single mapping case. Collard and Feautrier [CF93] address the multiple mapping case; however, only one dimensional iteration spaces are considered and many guards are ....

William Pugh and David Wonnacott. Experiences with constraint-based array dependence analysis. In Principles and Practice of Constraint Programming Workshop, Orcas Island, Washington, May 1994.

....answer. If the integers are relatively big, the errors may be acceptable. There are ways to ensure the correctness of the answer. As an integer shadow is not necessarily convex, a correct answer cannot be represented as a system of linear inequalities over the wanted variables. For instance, [Pug92, PW94] produce the usual real shadow, being complete, plus a second, dark shadow which is guaranteed to be correct. However, it is not complete. Integer solutions contained in the real shadow but not in the dark shadow must be enumerated and added disjunctively , which is expensive and requires new ....

W. Pugh and D. Wonnacott. Experiences with constraint-based array dependence analysis. In Proc. Principles and Practice of Constraint Programming, 1994.

....and notice is given that copying is by permission of the Association for Computing Machinery, Inc. ACM) To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior specific permission and or a fee. c fl 1998 ACM 0164 0925 98 0300 0388 5.00 2 Delta W. Pugh and D. Wonnacott for i : 2 to n do sum : 0.0 for l : 1 to i 1 do sum : sum A[l,i] B[l] endfor B[i] B[i] sum endfor (a) forall i : 1 to n do sum[i] 0.0 endfor for l : 1 to n 1 do B[l] B[l] sum[l] forall i : l 1 to n do sum[i] sum[i] A[l,i] B[l] endfor endfor (b) Fig. 1. a) From Petersen and Padua ....

Pugh, W. and Wonnacott, D. 1994a. Experiences with constraint-based array dependence analysis. In Principles and Practice of Constraint Programming, Second International Workshop. Lecture Notes in Computer Science, vol. 874. Springer-Verlag, Berlin, 312--325.

....poorly on moderate to large systems of constraints where the constraints are dense: each constraint involves many variables. However, the constraints we have seen in both dependence analysis and code generation are quite sparse, and Fourier elimination is quite efficient for sparse constraints [19]. Collard, Feautrier and Risset [7] show how PIP, a parametrized version of the Dual Simplex Method, can be used to solve the simple case. Collard and Feautrier [6] address the multiple mapping case; however, only one dimensional iteration spaces are considered and many guards are generated. They ....

William Pugh and David Wonnacott. Experiences with constraint-based array dependence analysis. In Principles and Practice of Constraint Programming Workshop, Orcas Island, Washington, May 1994.

No context found.

W. Pugh, and D. Wonnacott. Experience with Constraint-Based Array Dependence Analysis. Technical Report CS-TR-3371. University of Maryland (1994).

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC