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39
Restriction categories I: Categories of partial maps
 Theoretical Computer Science
, 2001
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On observed reproducibility in network configuration management
 Science of Computer Programming
, 2004
"... A rigorous language for discussing the issue of configuration management is currently lacking. To this end, we develop a simple statemachine model of configuration management. Observed behaviors comprise the state of a host and configuration processes accomplish state transitions. Using this langua ..."
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Cited by 11 (8 self)
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A rigorous language for discussing the issue of configuration management is currently lacking. To this end, we develop a simple statemachine model of configuration management. Observed behaviors comprise the state of a host and configuration processes accomplish state transitions. Using this language, we show that for one host in isolation and for some configuration processes, reproducibility of observed effect for a configuration process is a statically verifiable property of the process. Using configuration processes verified in this manner, we can efficiently identify latent preconditions that affect behavior among a population of hosts. Constructing configuration management tools with statically verifiable observed behaviors thus reduces the lifecycle cost of configuration management. 1
Seeking Closure in an Open World: A Behavioral Agent Approach to Configuration Management
 Proc. LISA XVII, USENIX Assoc
, 2003
"... Permission is granted for noncommercial reproduction of the work for educational or research purposes. ..."
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Cited by 11 (8 self)
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Permission is granted for noncommercial reproduction of the work for educational or research purposes.
On the algebraic structure of convergence
 IN: PROC. DSOM 2003
, 2003
"... Current selfhealing systems are built from “convergent” actions that only make repairs when necessary. Using an algebraic model of system administration, we challenge the traditional notion of “convergence” and propose a stronger definition with improved algebraic properties. Under the new defini ..."
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Cited by 9 (6 self)
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Current selfhealing systems are built from “convergent” actions that only make repairs when necessary. Using an algebraic model of system administration, we challenge the traditional notion of “convergence” and propose a stronger definition with improved algebraic properties. Under the new definition, the structure of traditional configuration management systems is a natural emergent property of the algebraic model. We discuss the impact of the new definition, as well as the changes required in current convergent tools in order to conform to the new definition.
Monoid generalizations of the Richard Thompson groups
 Mathematics ArXiv: math.GR/0704.0189
, 2007
"... The groups Gk,1 of Richard Thompson and Graham Higman can be generalized in a natural way to monoids, that we call Mk,1, and to inverse monoids, called Invk,1; this is done by simply generalizing bijections to partial functions or partial injective functions. The monoids Mk,1 have connections with c ..."
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The groups Gk,1 of Richard Thompson and Graham Higman can be generalized in a natural way to monoids, that we call Mk,1, and to inverse monoids, called Invk,1; this is done by simply generalizing bijections to partial functions or partial injective functions. The monoids Mk,1 have connections with circuit complexity (studied in another paper). Here we prove that Mk,1 and Invk,1 are congruencesimple for all k. Their Green relations J and D are characterized: Mk,1 and Invk,1 are J0simple, and they have k − 1 nonzero Dclasses. They are submonoids of the multiplicative part of the Cuntz algebra Ok. They are finitely generated, and their word problem over any finite generating set is in P. Their word problem is coNPcomplete over certain infinite generating sets. 1 ThompsonHigman monoids Since their introduction by Richard J. Thompson in the mid 1960s [25, 22, 26], the Thompson groups have had a great impact on infinite group theory. Graham Higman generalized the Thompson groups to an infinite family [17]. These groups and some of their subgroups have appeared in many contexts and have been widely studied; see for example [9, 5, 12, 7, 14, 15, 6, 8, 20]. The definition of the ThompsonHigman groups lends itself easily to generalizations to inverse
Finite aperiodic semigroups with commuting idempotents and generalizations
 Israel J. Math
, 2000
"... Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead ..."
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Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead
Semigroups, Rings, and Markov Chains
, 2000
"... We analyze random walks on a class of semigroups called "leftregular bands." These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multi ..."
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We analyze random walks on a class of semigroups called "leftregular bands." These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multiplicities. The methods lead to explicit formulas for the projections onto the eigenspaces. As examples of these semigroup walks, we construct a random walk on the maximal chains of any distributive lattice, as well as two random walks associated with any matroid. The examples include a qanalogue of the Tsetlin library. The multiplicities of the eigenvalues in the matroid walks are "generalized derangement numbers," which may be of independent interest.
Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited
, 2012
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The R and Lorders of the ThompsonHigman monoid Mk,1 and their complexity
, 812
"... We study the monoid generalization Mk,1 of the ThompsonHigman groups, and we characterize the R and the Lpreorder of Mk,1. Although Mk,1 has only one nonzero Jclass and k−1 nonzero Dclasses, the R and the Lpreorder are complicated; in particular, <R is dense (even within an Lclass), and ..."
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We study the monoid generalization Mk,1 of the ThompsonHigman groups, and we characterize the R and the Lpreorder of Mk,1. Although Mk,1 has only one nonzero Jclass and k−1 nonzero Dclasses, the R and the Lpreorder are complicated; in particular, <R is dense (even within an Lclass), and <L is dense (even within an Rclass). We study the computational complexity of the R and the Lpreorder. When inputs are given by words over a finite generating set of Mk,1, the R and the Lpreorder decision problems are in P. The main result of the paper is that over a “circuitlike ” generating set, the Rpreorder decision problem of Mk,1 is Π P 2complete, whereas the Lpreorder decision problem is coNPcomplete. We also prove related results about circuits: For combinational circuits, the surjectiveness problem is Π P 2complete, whereas the injectiveness problem is coNPcomplete. 1