A. Asperti and H. G. Mairson. Parallel beta reduction is not elementary recursive. In Conference Record of POPL '98: The 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 303--315, San Diego, California, 19--21 Jan. 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... 5 Polymorphic Iteration and Expressiveness Theorems Given two # terms of size n that are both typable in System I k , how hard is it to decide if they have the same normal form In this paper, we omit many technical details relating to the complexity analysis of this decision problem; see [Sta79, Mai92, AM98]. Instead, we outline the analysis at a high level. The technical details are not di#cult, and amount to a fairly mundane form of functional programming. The above decision problem is a simple form of detecting program equivalence. We can use the polymorphic iteration lemma to get lower bounds on ....

A. Asperti and H. G. Mairson. Parallel beta reduction is not elementary recursive. In Conference Record of POPL '98: The 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 303--315, San Diego, California, 19--21 Jan. 1998.

....terms can be deduced from the fact that any b step decreases the lengths of paths relative to the contracted redex and does not increase the lengths of other paths. A strong normalization proof for simply typed l calculus using a similar idea (but completely different technically) appears in [2]. Arrow decoration of hyperbalanced terms is useful for other purposes too. For example, it allows us to develop a static garbage collection algorithm; that is, we can detect all inessential [11] subterms in a hyperbalanced term M without any transformation of M, and inessential subterms can be ....

ASPERTI, A., MAIRSON H.G., Parallel beta reduction is not elementary recursive. In Proc. of ACM Symposium on Principles of Programming Languages (POPL), 1998.

....bounded creation degree are allowed for contraction are terminating. Klop [35] proves this so called Decreasing RedexLabelling Lemma via interpretation into the I calculus. The lemma has been used in strong normalization proofs of the simply typed calculus by Klop [35] by Asperti and Meirson [3] and by the authors in [34] Gandy [20] Nederpelt [42] and Klop [35] were the rst to use interpretation of 2 (typed or untyped) calculi into the I calculus for normalization proofs. Nederpelt s and Klop s translations enable to infer strong normalization from normalization since in ....

A. Asperti, H.G. Mairson. Parallel beta reduction is not elementary recursive. ACM Symposium on Principles of Programming Languages, POPL'98, 1998, p. 303-315.

....with the computational models used in complexity theory. We think that the interest in the definition of a suitable notion of cost and of complexity classes for sharing computations is even more appealing after the results of Asperti [Asp96] Lawall and Mairson [LM96] and Asperti and Mairson [AM98] showing that L evy families cannot be the cost model of calculus reductions. Acknowledgments I wish to thank Simone Martini who supervised my thesis and always encouraged me persisting, even when things seemed to get everyday more involved; Andrea Asperti who introduced me to the intriguing ....

Andrea Asperti and Harry Mairson. Parallel beta reduction is not elementary recursive. In Conference Record of POPL '98: The 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, San Diego, California, 1998.

....a conversation with incomplete proofs and basic intuitions. For those who from semantics recoil, recall: this is algorithm analysis, establishing the correctness of an incremental interpreter. Related complexity analysis, both of Lamping s algorithm and the problem, can be found in [6, 4]. 2 Linear # terms The best place to start representing the essence of the full problem, but in miniature is with linear # terms: every variable must occur exactly once. Church numerals #s.#z.s z are ruled out (s may occur more than once or not at all) also Boolean truth values (recall ....

A. Asperti and H. G. Mairson. Parallel beta reduction is not elementary recursive. Information and Computation, 170:49--80, 2001.

....a new systematic basis on which to optimize the sharing of continuations. We wish to emphasize that the Asperti Mairson theorem on the complexity of parallel reduction does not say that such optimal reduction is inecient only that the parallel reduction cannot be considered a unit cost operation [3]. In summary, all of the translations we outline possess a simple graph reduction on translated terms (cut elimination for linear logic) a consistent semantics that is preserved by reduction (geometry of interaction, via the so called context semantics of Gonthier [14] and a mechanism whereby ....

A. Asperti and H.G. Mairson. Parallel beta reduction is not elementary recursive. In Conference Record of POPL '98: The 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 303-315, San Diego, California, 19-21 January 1998.

....his breakthrough other variants of optimal reducers have been proposed, especially by Gonthier, Abadi and L evy [GnAL92a] and Asperti [Asp95] We will refer to all of them as the optimal sharing graph approach. All these variants share a common core the abstract algorithm in the terminology of [AM98] and di er in the way they implement the bookkeeping work needed to maintain the families. The algorithms are described as elegant graph rewriting systems, where any rule rewrites only a pair of facing nodes (and then it can be easily implemented as a constant time operation) The abstract ....

....perform both duplication (in the abstract algorithm) and bookkeeping. Is it possible to bound the total work as a ( xed) function of the number of shared reductions It is this question that has been behind several contributions by Asperti, Lawall, and Mairson [Asp96, LM96, LM97] culminated in [AM98]. De ne the Kalm ar elementary functions K (n) as K0 (n) n and K 1 (n) 2 K (n) Then [AM98] shows that there are terms that can be normalized with n shared reductions, and for which the total work needed to reach the normal form with any algorithm (and hence with any optimal ....

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Andrea Asperti and Harry G. Mairson. Parallel beta reduction is not elementary recursive. In Conference Record of POPL '98: The 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 303{ 315, San Diego, California, 19-21 January 1998.

....to true. 5 Polymorphic Iteration and Expressiveness Theorems Given two terms of size n that are both typable in System I k , how hard is it to decide if they have the same normal form In this paper, we omit many technical details relating to the complexity analysis of this decision problem; see [Sta79, Mai92, AM98]. Instead, we outline the analysis at a high level. The technical details are not difficult, and amount to a fairly mundane form of functional programming. The above decision problem is a simple form of detecting program equivalence. We can use the polymorphic iteration lemma to get lower bounds ....

A. Asperti and H. G. Mairson. Parallel beta reduction is not elementary recursive. In Conference Record of POPL '98: The 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 303--315, San Diego, California, 19--21 Jan. 1998.

No context found.

A. Asperti and H. G. Mairson. Parallel beta reduction is not elementary recursive. In Conference Record of POPL '98: The 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 303--315, San Diego, California, 19--21 Jan. 1998.

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