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Searching Constant Width Mazes Captures the AC° Hierarchy
 In Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
, 1997
"... We show that searching a width /' maze is complete for II, i.e., for the /"th level of the AC hierarchy. Equivalently, stconnectivity for width /' grid graphs is complete for II. As an application, we show that there is a data structure solving dynamic stconnectivity for constant width grid gr ..."
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Cited by 22 (4 self)
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We show that searching a width /' maze is complete for II, i.e., for the /"th level of the AC hierarchy. Equivalently, stconnectivity for width /' grid graphs is complete for II. As an application, we show that there is a data structure solving dynamic stconnectivity for constant width grid graphs with time bound O (log log n) per operation on a random access machine. The dynamic algorithm is derived from the parallel one in an indirect way using algebraic tools.
Relational Reasoning about Contexts
 HIGHER ORDER OPERATIONAL TECHNIQUES IN SEMANTICS, PUBLICATIONS OF THE NEWTON INSTITUTE
, 1998
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Foundational and mathematical uses of higher types
 REFLECTIONS ON THE FOUNDATIONS OF MATHEMATICS: ESSAY IN HONOR OF SOLOMON FEFERMAN
, 1999
"... In this paper we develop mathematically strong systems of analysis in higher types which, nevertheless, are prooftheoretically weak, i.e. conservative over elementary resp. primitive recursive arithmetic. These systems are based on noncollapsing hierarchies ( n WKL+ ; n WKL+ ) of principles ..."
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Cited by 11 (4 self)
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In this paper we develop mathematically strong systems of analysis in higher types which, nevertheless, are prooftheoretically weak, i.e. conservative over elementary resp. primitive recursive arithmetic. These systems are based on noncollapsing hierarchies ( n WKL+ ; n WKL+ ) of principles which generalize (and for n = 0 coincide with) the socalled `weak' König's lemma WKL (which has been studied extensively in the context of second order arithmetic) to logically more complex tree predicates. Whereas the second order context used in the program of reverse mathematics requires an encoding of higher analytical concepts like continuous functions F : X ! Y between Polish spaces X;Y , the more exible language of our systems allows to treat such objects directly. This is of relevance as the encoding of F used in reverse mathematics tacitly yields a constructively enriched notion of continuous functions which e.g. for F : IN ! IN can be seen (in our higher order context)
On the Computational Content of the BolzanoWeierstraß Principle
, 2009
"... We will apply the methods developed in the field of ‘proof mining’ to the BolzanoWeierstraß theorem BW and calibrate the computational contribution of using this theorem in proofs of combinatorial statements. We provide an explicit solution of the Gödel functional interpretation (combined with nega ..."
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Cited by 4 (4 self)
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We will apply the methods developed in the field of ‘proof mining’ to the BolzanoWeierstraß theorem BW and calibrate the computational contribution of using this theorem in proofs of combinatorial statements. We provide an explicit solution of the Gödel functional interpretation (combined with negative translation) as well as the monotone functional interpretation of BW for the product space ∏i∈N[−k i, k i] (with the standard product metric). This results in optimal program and bound extraction theorems for proofs based on fixed instances of BW, i.e. for BW applied to fixed sequences in ∏i∈N[−k i, k i].
Things that can and things that can't be done in PRA
, 1998
"... It is wellknown by now that large parts of (nonconstructive) mathematical reasoning can be carried out in systems T which are conservative over primitive recursive arithmetic PRA (and even much weaker systems). On the other hand there are principles S of elementary analysis (like the BolzanoW ..."
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Cited by 3 (1 self)
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It is wellknown by now that large parts of (nonconstructive) mathematical reasoning can be carried out in systems T which are conservative over primitive recursive arithmetic PRA (and even much weaker systems). On the other hand there are principles S of elementary analysis (like the BolzanoWeierstra principle, the existence of a limit superior for bounded sequences etc.) which are known to be equivalent to arithmetical comprehension (relative to T ) and therefore go far beyond the strength of PRA (when added to T ). In this paper
Formal Modeling and Analysis of an Audio/Video Protocol: An Industrial . . .
, 1997
"... A formal and automatic verification of a reallife protocol is presented. The protocol, about 2800 lines of assembler code, has been used in products from the audio/video company Bang & Olufsen throughout more than a decade, and its purpose is to control the transmission of messages between audio ..."
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Cited by 2 (0 self)
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A formal and automatic verification of a reallife protocol is presented. The protocol, about 2800 lines of assembler code, has been used in products from the audio/video company Bang & Olufsen throughout more than a decade, and its purpose is to control the transmission of messages between audio/video components over a single bus. Such communications may collide, and one essential purpose of the protocol is to detect such collisions. The functioning is highly dependent on realtime considerations. Though the protocol was known to be faulty in that messages were lost occasionally, the protocol was too complicated in order for Bang & Olufsen to locate the bug using normal testing. However, using the realtime verification tool UPPAAL, an error trace was automatically generated, which caused the detection of "the error" in the implementation. The error was corrected and the correction was automatically proven correct, again using UPPAAL. A future, and more automated, version of the protocol, where this error is fatal, will incorporate the correction. Hence, this work is an elegant demonstration of how model checking has had an impact on practical software development. The effort of modeling this protocol has in addition generated a number of suggestions for enriching the UPPAAL language. Hence, it's also an excellent example of the reverse impact.