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The Encyclopedia of Integer Sequences
"... This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs ..."
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This article gives a brief introduction to the OnLine Encyclopedia of Integer Sequences (or OEIS). The OEIS is a database of nearly 90,000 sequences of integers, arranged lexicographically. The entry for a sequence lists the initial terms (50 to 100, if available), a description, formulae, programs to generate the sequence, references, links to relevant web pages, and other
Oblivious and adaptive strategies for the majority and plurality problems
"... In the wellstudied Majority problem, we are given a set of n balls colored with two or more colors, and the goal is to use the minimum number of color comparisons to find a ball of the majority color (i.e., a color that occurs for more than ⌈n/2⌉ times). The Plurality problem has exactly the same ..."
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Cited by 4 (1 self)
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In the wellstudied Majority problem, we are given a set of n balls colored with two or more colors, and the goal is to use the minimum number of color comparisons to find a ball of the majority color (i.e., a color that occurs for more than ⌈n/2⌉ times). The Plurality problem has exactly the same setting while the goal is to find a ball of the dominant color (i.e., a color that occurs most often). Previous literature regarding this topic dealt mainly with adaptive strategies, whereas in this paper we focus more on the oblivious (i.e., nonadaptive) strategies. Given that our strategies are oblivious, we establish a linear upper bound for the Majority problem with arbitrarily many different colors. We then show that the Plurality problem is significantly more difficult by establishing quadratic lower and upper bounds. In the end, we also discuss some generalized upper bounds for adaptive strategies in the kcolor Plurality problem.
On Alan Turing and the Origins of Digital Computers
 Machine Intelligence
, 1972
"... This paper documents an investigation into the role that the late Alan Turing played in the development of electronic computers. Evidence is presented that during the war he was associated with a group that designed and built a series of special purpose electronic computers, which were in at least a ..."
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This paper documents an investigation into the role that the late Alan Turing played in the development of electronic computers. Evidence is presented that during the war he was associated with a group that designed and built a series of special purpose electronic computers, which were in at least a limited sense ‘program controlled’, and that the origins of several postwar general purpose computer projects in Britain can be traced back to these wartime computers.
Iterating invertible binary transducers
"... Abstract. We study iterated transductions defined by a class of invertible transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the ..."
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Abstract. We study iterated transductions defined by a class of invertible transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata. 1
A NonMessingUp Phenomenon for Posets
, 2005
"... We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along both sets of chains, the labels of the chains in the first s ..."
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We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along both sets of chains, the labels of the chains in the first set remain sorted. We also characterize posets with more restrictive sorting properties. 1
Finding Favorites
"... We investigate a new type of informationtheoretic identification problem, suggested to us by Alan Taylor. In this problem we are given a set of items, more than half of which share a common “good ” value. The other items have various other values which are called “bad”. The only method we have for ..."
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We investigate a new type of informationtheoretic identification problem, suggested to us by Alan Taylor. In this problem we are given a set of items, more than half of which share a common “good ” value. The other items have various other values which are called “bad”. The only method we have for gaining information about the items’ values is to ask whether two items share the same value. We can assume there is an oracle which always answers each such query truthfully. Our goal is to identify at least one good item, i.e., an item which is guaranteed to have a good value, using a minimum possible number of queries. We will establish upper and lower bounds for the number of queries needed for both adaptive as well as oblivious strategies. The practical context in which this problem arose was in connection with trying to identify a good sensor from a set of sensors in which some are nonoperational or corrupted, for example, where it was desired to minimize the amount of intercommunication used in doing so. 1
Flipping Pebbles
"... Suppose you have a sequence of pebbles, blue on one side and white on the other. Starting at the leftmost pebble, flip (some of) them over according to the following rule: Flip the current pebble. If it is now whiteside up, skip over the next one. Otherwise, skip over the next two pebbles. Repeat t ..."
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Suppose you have a sequence of pebbles, blue on one side and white on the other. Starting at the leftmost pebble, flip (some of) them over according to the following rule: Flip the current pebble. If it is now whiteside up, skip over the next one. Otherwise, skip over the next two pebbles. Repeat till you fall off the end. Let us call this the toggle operation. Thus, the toggle operation turns the following pebble sequence into Admittedly, it is a bit of a stretch to refer to this operation as a game. But, as in Conway’s GameofLife [5], interesting questions arise when we iterate. Figure 1 shows the result of applying our rule repeatedly to a sequence of 20 pebbles. Note that the behavior of the first few pebbles is simply periodic, but more complicated patterns emerge further down the line. We are trying to understand exactly how complicated these orbits are. A moment’s thought reveals that the toggle operation is reversible, so the orbit of any sequence must be a cycle. A few computational experiments suggest that the length of the cycle associated with a sequence of length n is about 2 n/2 and thus has exponential length. This leads to a natural
and
"... We study iterated transductions defined by a class of inverse transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of ..."
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We study iterated transductions defined by a class of inverse transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.
and
"... We study iterated transductions defined by a class of inverse transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of ..."
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We study iterated transductions defined by a class of inverse transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.
Running head is “TRANSFORMATIONS ON WORDS” Proofs should be sent to
"... The purpose of this paper is to give the description of a single algorithm that specializes into several classical transformations derived on words, namely the CartierFoata transform, its contextual extension due to Han and the two kextensions proposed by Clarke and Foata. 3 List of Symbols symbol ..."
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The purpose of this paper is to give the description of a single algorithm that specializes into several classical transformations derived on words, namely the CartierFoata transform, its contextual extension due to Han and the two kextensions proposed by Clarke and Foata. 3 List of Symbols symbol location type comment c R(c) boldface c ℓ sΦ q ℓ, ℓexcedances, denℓ, Φ sΦ ell q T