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Optimizing Ackermann's function by incrementalization

Yanhong A. Liu, Scott D. Stoller
2003 SIGPLAN notices  
This paper describes a formal derivation of an 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.  ... 
doi:10.1145/966049.777398 fatcat:fcp5c2zbmjfmhouxlo7xw53wt4

Optimizing Ackermann's function by incrementalization

Yanhong A. Liu, Scott D. Stoller
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 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.  ... 
doi:10.1145/777388.777398 dblp:conf/pepm/LiuS03 fatcat:2fr5qkbo6ngylllyv3daqz5boa

Efficient handling of data structures in definitional languages

Boleslaw K. Szymanski, Noah S. Prywes
1988 Science of Computer Programming  
The method is exemplified 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.  ... 
doi:10.1016/0167-6423(88)90050-0 fatcat:ejjhnzy2gvgsrbfaib4kufrxny

Model-based Theory Combination

Leonardo de Moura, Nikolaj Bjørner
2008 Electronical Notes in Theoretical Computer Science  
This paper introduces a combination method that 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.  ... 
doi:10.1016/j.entcs.2008.04.079 fatcat:ylqbd7k64rgjvcrhsy27nyef4y

How to call procedures, or second thoughts on Ackermann's function

B. A. Wichmann
1977 Software, Practice & Experience  
Various problems have been encountered in using 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] .  ... 
doi:10.1002/spe.4380070303 fatcat:dvbly5jtqzh45etfufeixtv7qq

Page 7783 of Mathematical Reviews Vol. , Issue 96m [page]

1996 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.  ... 

The MathSAT 3 System [chapter]

Marco Bozzano, Roberto Bruttomesso, Alessandro Cimatti, Tommi Junttila, Peter van Rossum, Stephan Schulz, Roberto Sebastiani
2005 Lecture Notes in Computer Science  
All these optimizations can be disabled/enabled by the user.  ...  Arithmetic function symbols are treated as fully uninterpreted.  ... 
doi:10.1007/11532231_23 fatcat:svs4vtnxqvhczpyl7u6xe6fowe

To Ackermann-ize or Not to Ackermann-ize? On Efficiently Handling Uninterpreted Function Symbols in $\mathit{SMT}(\mathcal{EUF} \cup \mathcal{T})$ [chapter]

Roberto Bruttomesso, Alessandro Cimatti, Anders Franzén, Alberto Griggio, Alessandro Santuari, Roberto Sebastiani
2006 Lecture Notes in Computer Science  
For this case, an alternative approach is to eliminate first all uninterpreted 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  ... 
doi:10.1007/11916277_38 fatcat:ucne6c6tljadva7tpsqn26g2jq

Page 3857 of Mathematical Reviews Vol. , Issue 98F [page]

1998 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  ... 

Page 3507 of Mathematical Reviews Vol. , Issue 94f [page]

1994 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.  ... 

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).  ... 

Page 3385 of Mathematical Reviews Vol. , Issue 91F [page]

1991 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).  ... 

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.  ... 

A tuning algorithm for a sliding mode controller of buildings with ATMD [article]

Antonio Concha, Suresh Thenozhi, Ramón O. Jiménez-Betancourt, S. K. Gadi
2020 arXiv   pre-print
This paper proposes an automatic tuning algorithm for a sliding mode controller (SMC) based on the 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.  ... 
arXiv:2012.05966v1 fatcat:muqdvxodrfcjdizcfvcuybscve

Optimized Live Heap Bound Analysis [chapter]

Leena Unnikrishnan, Scott D. Stoller, Yanhong A. Liu
2002 Lecture Notes in Computer Science  
This paper describes a general approach for 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.  ... 
doi:10.1007/3-540-36384-x_9 fatcat:lyjogi4br5akzn7xxma2ecmbam
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