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Applications of Brzozowski derivatives to XML Schema processing
 IN: EXTREME MARKUP LANGUAGES 2005, IDEALLIANCE
, 2005
"... Given a regular language L, the Brzozowski derivative of L with respect to some string s is a regular expression which defines what strings can follow s in strings appearing in L. The calculation of Brzozowski derivatives is a convenient and beautiful tool for the algebraic manipulation of content m ..."
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Cited by 3 (0 self)
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Given a regular language L, the Brzozowski derivative of L with respect to some string s is a regular expression which defines what strings can follow s in strings appearing in L. The calculation of Brzozowski derivatives is a convenient and beautiful tool for the algebraic manipulation of content
SIS: A System for Sequential Circuit Synthesis
, 1992
"... SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logiclevel description of a sequential circuit, it produces an optimized netlist in the target technology while preserving the sequential inputoutput b ..."
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Cited by 514 (41 self)
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SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logiclevel description of a sequential circuit, it produces an optimized netlist in the target technology while preserving the sequential inputoutput behavior. Many different programs and algorithms have been integrated into SIS, allowing the user to choose among a variety of techniques at each stage of the process. It is built on top of MISII [5] and includes all (combinational) optimization techniques therein as well as many enhancements. SIS serves as both a framework within which various algorithms can be tested and compared, and as a tool for automatic synthesis and optimization of sequential circuits. This paper provides an overview of SIS. The first part contains descriptions of the input specification, STG (state transition graph) manipulation, new logic optimization and verification algorithms, ASTG (asynchronous signal transition graph) manipulation, and synthesis for PGA’s (programmable gate arrays). The second part contains a tutorial example illustrating the design process using SIS.
On a problem of Brzozowski and Fich
"... The problem of decidability of membership in the semidirect product Sl L of the pseudovarieties Sl of all finite semilattices and L of all finite L trivial semigroups has been around since 1984. This paper discusses several developments motivated by this question and leading to a proof that set ..."
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The problem of decidability of membership in the semidirect product Sl L of the pseudovarieties Sl of all finite semilattices and L of all finite L trivial semigroups has been around since 1984. This paper discusses several developments motivated by this question and leading to a proof that settles it affirmatively. 1 Introduction The historical importance of certain "test problems" in the development of Mathematics is probably easily acknowledged in view of examples such as the squaring of the circle or, more recently, Fermat's "last theorem" or the fourcolour map conjecture. In all such examples, one may say that the developments they led to have far reaching consequences, even if the results themselves are not much more than curiosities. Each researcher tends to have a personal set of test problems in mind guiding contributions to the theories of her/his own interest. When a problem is chosen, one usually thinks that one should be able to solve it. Sometimes, one sees immed...
Derivatives of regular expressions
 JOURNAL OF THE ACM
, 1964
"... Abstract. Kleene's regular expressions, which can be used for describing sequential circuits, were defined using three operators (union, concatenation and iterate) on sets of sequences. Word descriptions of problems can be more easily put in the regular expression language if the language is en ..."
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Cited by 297 (10 self)
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the notion of a derivative of a regular expression is introduced and the properties of derivatives are discussed. This leads, in a very natural way, to the construction of a state diagram from a regular expression containing any number of logical operators.
Brzozowski’s algorithm (co)algebraically
"... Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctn ..."
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Cited by 11 (3 self)
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Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its
AlgebraCoalgebra Duality in Brzozowski’s Minimization Algorithm
"... We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simpl ..."
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Cited by 7 (2 self)
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We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a
Brzozowski’s and upto algorithms for must testing?
"... Abstract. Checking language equivalence (or inclusion) of finite automata is a classical problem in Computer Science, which has recently received a renewed interest and found novel and more effective solutions, such as approaches based on antichains or bisimulations upto. Several notions of equiv ..."
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Abstract. Checking language equivalence (or inclusion) of finite automata is a classical problem in Computer Science, which has recently received a renewed interest and found novel and more effective solutions, such as approaches based on antichains or bisimulations upto. Several notions of equivalence (or preorder) have been proposed for the analysis of concurrent systems. Usually, the problem of checking these equivalences is reduced to checking bisimilarity. In this paper, we take a different approach and propose to adapt algorithms for language equivalence to check one prime equivalence in concurrency theory, must testing semantics. To achieve this transfer of technology from language to must semantics, we take a coalgebraic outlook at the problem. 1
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