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Optimizing Ackermann's function by incrementalization

2003
*
SIGPLAN notices
*

This paper describes a formal derivation of an

doi:10.1145/966049.777398
fatcat:fcp5c2zbmjfmhouxlo7xw53wt4
*optimized**Ackermann's**function*following a general and systematic method based on*incrementalization*. ... The method identifies an appropriate input*increment*operation and computes the*function**by*repeatedly performing an*incremental*computation at the step of the*increment*. ... We also thank Alan Mycroft for his interest in*incrementalization*and his specific questions about*Ackermann's**function*that eventually led us to*optimize*it using*incrementalization*. ...##
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Optimizing Ackermann's function by incrementalization

2003
*
Proceedings of the 2003 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation - PEPM '03
*

This paper describes a formal derivation of an

doi:10.1145/777388.777398
dblp:conf/pepm/LiuS03
fatcat:2fr5qkbo6ngylllyv3daqz5boa
*optimized**Ackermann's**function*following a general and systematic method based on*incrementalization*. ... The method identifies an appropriate input*increment*operation and computes the*function**by*repeatedly performing an*incremental*computation at the step of the*increment*. ... We also thank Alan Mycroft for his interest in*incrementalization*and his specific questions about*Ackermann's**function*that eventually led us to*optimize*it using*incrementalization*. ...##
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Efficient handling of data structures in definitional languages

1988
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Science of Computer Programming
*

The method is exemplified

doi:10.1016/0167-6423(88)90050-0
fatcat:ejjhnzy2gvgsrbfaib4kufrxny
*by*its application to the non-recursive iteration computation of the*Ackermann's**function*. ... First, criteria are presented for recognizing structures that may be*optimized*. Then, a transformation that removes iterations implied*by*the operations on*incremental*structures is described. ... Owing to it,*incremental*structures can also be*optimized*. ...##
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Model-based Theory Combination

2008
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Electronical Notes in Theoretical Computer Science
*

This paper introduces a combination method that

doi:10.1016/j.entcs.2008.04.079
fatcat:ylqbd7k64rgjvcrhsy27nyef4y
*incrementally*reconciles models maintained*by*each theory. We evaluate the practicality and efficiency of this approach. ... Efficient and*incremental*congruence closure based procedures are described in [7, 13] . ... Model based theory combination seems to be more robust than DTC or*Ackermann's*reduction. In these benchmarks, the average number of shared equalities propagated*by*Z3 using M-Propagate was 2.46. ...##
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How to call procedures, or second thoughts on Ackermann's function

1977
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Software, Practice & Experience
*

Various problems have been encountered in using

doi:10.1002/spe.4380070303
fatcat:dvbly5jtqzh45etfufeixtv7qq
*Ackermann's**function*to measure the efficiency of procedure calIs in System Implementation Languages. ... A surprising result from the analysis is that implementation quality is far more important than the overheads implied*by*language design. ... Measurements using*Ackermann's**function*have been made with this in mind [1] . ...##
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Page 7783 of Mathematical Reviews Vol. , Issue 96m
[page]

1996
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Mathematical Reviews
*

in O(na(n)) expected time, where a(n) is the inverse of

*Ackermann’s**function*. The second algorithm constructs a single cell in an arrangement of n triangles in R® in O(n? log’ n) expected time. ... 7783 characterised*by*several environmental factors (e.g., number of agents, completeness of information, purpose of the negotiation) and the agents’ utility*functions*. ...##
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The MathSAT 3 System
[chapter]

2005
*
Lecture Notes in Computer Science
*

All these

doi:10.1007/11532231_23
fatcat:svs4vtnxqvhczpyl7u6xe6fowe
*optimizations*can be disabled/enabled*by*the user. ... Arithmetic*function*symbols are treated as fully uninterpreted. ...##
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To Ackermann-ize or Not to Ackermann-ize? On Efficiently Handling Uninterpreted Function Symbols in $\mathit{SMT}(\mathcal{EUF} \cup \mathcal{T})$
[chapter]

2006
*
Lecture Notes in Computer Science
*

For this case, an alternative approach is to eliminate first all uninterpreted

doi:10.1007/11916277_38
fatcat:ucne6c6tljadva7tpsqn26g2jq
*function*symbols*by*means of*Ackermann's*expansion, and then to solve the resulting SMT (T 2 ) problem. ... We propose a simple technique for estimating a priori the costs and benefits, in terms of the size of the search space of an SMT tool, of applying*Ackermann's*expansion to all or part of the*function*symbols ... SMT(EUF ∪ T ) via*Ackermann's*expansion When one of the theories T i is EUF , another possible approach to the SMT(T 1 ∪ T 2 ) problem is to eliminate uninterpreted*function*symbols*by*means of*Ackermann's*...##
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Page 3857 of Mathematical Reviews Vol. , Issue 98F
[page]

1998
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Mathematical Reviews
*

inverse of

*Ackermann’s**function*. ... We show that the mathemati- cal model for register management*by*an algebraic compiler is a graph coloring problem in which an*optimally*colored graph is obtained*by*composing*optimally*colored subgraphs ...##
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Page 3507 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
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Mathematical Reviews
*

It runs in O((d +n) log” n) time and uses O(na(n)) space, where d is the size of the final display, and a(n) is a (very slowly growing)

*functional*inverse of*Ackermann’s**function*. ... 3507*optimization*”, PhD. ...##
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Page 3304 of Mathematical Reviews Vol. , Issue 2001E
[page]

2001
*
Mathematical Reviews
*

Here, a(n) is the inverse of

*Ackermann’s**function*.” Therese C. Biedl (3-WTRL-C; Waterloo, ON) 65 NUMERICAL ANALYSIS 2001¢:65030 65D18 68U05 Garcia-Lopez, J. ... If y:C" — G is a recovery map, the recovery error is given*by*e(y, S, N,6) := sup{|S(f) — ply): f € B, lly— Nf|| <6}. The*optimal*recovery error is e(S, N,d) = inf, e(y, S, N,d). ...##
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Page 3385 of Mathematical Reviews Vol. , Issue 91F
[page]

1991
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Mathematical Reviews
*

., disjoint convex sites with the Eu- clidean distance

*function*. Abstract Voronoi diagrams are given*by*a family of bisecting curves and were recently introduced*by*R. ... -'/2B(n)) for d=2, d=3 and d >4, respectively (where f(n) is related to the inverse of*Ackermann’s**function*), whereas the algorithm for arbitrarily oriented rectangles takes time O(n? log n). ...##
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Page 2237 of Mathematical Reviews Vol. , Issue 91D
[page]

1991
*
Mathematical Reviews
*

’s

*function*. ... The algorithm improves on the O(Mnlog Mn) bound previously established for this problem and is easily seen to be*optimal*. The algorithm solves the problem posed*by*Nurmi and*by*Toussaint. ...##
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A tuning algorithm for a sliding mode controller of buildings with ATMD
[article]

2020
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arXiv
*
pre-print

This paper proposes an automatic tuning algorithm for a sliding mode controller (SMC) based on the

arXiv:2012.05966v1
fatcat:muqdvxodrfcjdizcfvcuybscve
*Ackermann's*formula, that attenuates the structural vibrations of a seismically excited building equipped ... The switching gain and sliding surface of the SMC are designed through the proposed tuning algorithm to suppress the structural vibrations*by*minimizing either the top floor displacement or the control ...*Ackermann's*formula and its robustness against friction uncertainty was demonstrated. ...##
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Optimized Live Heap Bound Analysis
[chapter]

2002
*
Lecture Notes in Computer Science
*

This paper describes a general approach for

doi:10.1007/3-540-36384-x_9
fatcat:lyjogi4br5akzn7xxma2ecmbam
*optimized*live heap space and live heap space-bound analyses for garbage-collected languages. ... The*optimization*drastically improves the analysis efficiency. The analyses have been implemented and experimental results confirm their accuracy and efficiency. ... We applied live heap space analysis handling tail call*optimization*to tailrecursive versions of reverse, insertion sort, selection sort and an*optimized**Ackermann's**function*. ...
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