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An Exercise in Programming in PA: Fast Growing Hierarchy Functions
"... this paper is to illustrate that the techniques of computer programming can be used in mathematical logic. We apply the wellknown list processing techniques to the task of introducing into PA (i.e. programming) the functions F of the Fast Growing Hierarchy (see [LW70,Wa70,Wa72,Ro84]). Although comp ..."
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this paper is to illustrate that the techniques of computer programming can be used in mathematical logic. We apply the wellknown list processing techniques to the task of introducing into PA (i.e. programming) the functions F of the Fast Growing Hierarchy (see [LW70,Wa70,Wa72,Ro84]). Although
The OrdinalRecursive Complexity of TimedArc Petri Nets, Data Nets, and Other Enriched Nets
, 2013
"... Abstract—We show how to reliably compute fastgrowing functions with timedarc Petri nets and data nets. This construction provides ordinalrecursive lower bounds on the complexity of the main decidable properties (safety, termination, regular simulation, etc.) of these models. Since these new lower ..."
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Cited by 1 (1 self)
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lower bounds match the upper bounds that one can derive from wqo theory, they precisely characterise the computational power of these socalled “enriched ” nets. Index Terms—Complexity theory, fastgrowing hierarchy, formal verification, Petri nets, wellstructured systems I.
An adaptive, nonuniform cache structure for wiredelay dominated onchip caches
 In International Conference on Architectural Support for Programming Languages and Operating Systems
, 2002
"... Growing wire delays will force substantive changes in the designs of large caches. Traditional cache architectures assume that each level in the cache hierarchy has a single, uniform access time. Increases in onchip communication delays will make the hit time of large onchip caches a function of a ..."
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Cited by 314 (39 self)
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Growing wire delays will force substantive changes in the designs of large caches. Traditional cache architectures assume that each level in the cache hierarchy has a single, uniform access time. Increases in onchip communication delays will make the hit time of large onchip caches a function
An extremely sharp phase transition threshold for the slow growing hierarchy
 Mathematical Structures in Computer Science
"... Abstract. We investigate natural systems of fundamental sequences for ordinals below the Howard Bachmann ordinal and study growth rates of the resulting slow growing hierarchies. We consider a specific assignment of fundamental sequences which depends on a non negative real number ε. We show that t ..."
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Cited by 4 (3 self)
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that the resulting slow growing hierarchy is eventually dominated by a fixed elementary recursive function if ε is equal to zero. We show further that the resulting slow growing hierarchy exhausts the provably recursive functions of ID1 if ε is strictly greater than zero. Finally we show that the resulting fast
Goodstein’s function
"... Goodstein’s function G: N → N is an example of a fast growing recursive function. Introduced in 1944 by R. L. Goodstein [9], Kirby and Paris [11] showed in 1982, using model theoretic techniques, that Goodstein’s result that G is total, i.e., that G(n) is defined for all n ∈ N, is not a theorem of ..."
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of first order Peano Arithmetic. We compute Goodstein’s function in terms of the LöbWainer fast growing hierarchy of functions; from this and standard proof theoretic results about this hierarchy, the KirbyParis result follows immediately. We also compute the functions of the Hardy hierarchy in terms
ProofTheoretic Analysis of Termination Proofs
 APAL
, 1994
"... Introduction In [Cichon 1990] the question has been discussed (and investigated) whether the order type of a termination ordering places a bound on the lengths of reduction sequences in rewrite systems reducing under . It was claimed that at least in the cases of the recursive path ordering rpo a ..."
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Cited by 11 (0 self)
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are bounded by some function F from the fastgrowing hierarchy below ! . Unfort
What's so special about Kruskal's Theorem AND THE ORDINAL Γ0? A SURVEY OF SOME RESULTS IN PROOF THEORY
 ANNALS OF PURE AND APPLIED LOGIC, 53 (1991), 199260
, 1991
"... This paper consists primarily of a survey of results of Harvey Friedman about some proof theoretic aspects of various forms of Kruskal’s tree theorem, and in particular the connection with the ordinal Γ0. We also include a fairly extensive treatment of normal functions on the countable ordinals, an ..."
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Cited by 56 (2 self)
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, and we give a glimpse of Veblen hierarchies, some subsystems of secondorder logic, slowgrowing and fastgrowing hierarchies including Girard’s result, and Goodstein sequences. The central theme of this paper is a powerful theorem due to Kruskal, the “tree theorem”, as well as a “finite miniaturization
COMPLEXITY HIERARCHIES BEYOND ELEMENTARY
, 2013
"... We introduce a hierarchy of fastgrowing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a nonelementary complexity, which occur naturally in logic, combinatorics, formal ..."
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Cited by 11 (4 self)
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We introduce a hierarchy of fastgrowing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a nonelementary complexity, which occur naturally in logic, combinatorics
Scalable Feature Selection, Classification and Signature Generation for Organizing Large Text Databases Into Hierarchical Topic Taxonomies
, 1998
"... We explore how to organize large text databases hierarchically by topic to aid better searching, browsing and filtering. Many corpora, such as internet directories, digital libraries, and patent databases are manually organized into topic hierarchies, also called taxonomies. Similar to indices for r ..."
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Cited by 131 (8 self)
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We explore how to organize large text databases hierarchically by topic to aid better searching, browsing and filtering. Many corpora, such as internet directories, digital libraries, and patent databases are manually organized into topic hierarchies, also called taxonomies. Similar to indices
Growing a Bag of Systems Tree for Fast and Accurate Classification
"... The bagofsystems (BoS) representation is a descriptor of motion in a video, where dynamic texture (DT) codewords represent the typical motion patterns in spatiotemporal patches extracted from the video. The efficacy of the BoS descriptor depends on the richness of the codebook, which directly dep ..."
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Cited by 4 (2 self)
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depends on the number of codewords in the codebook. However, for even modest sized codebooks, mapping videos onto the codebook results in a heavy computational load. In this paper we propose the BoS Tree, which constructs a bottomup hierarchy of codewords that enables efficient mapping of videos
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