Journal ArticleDOI
Signal Flow Graph Techniques for Sequential Circuit State Diagrams
TLDR
It is shown that the methods of signal flow graph theory, with the proper interpretation, apply to state diagrams of sequential circuits and leads to a simple algorithm for obtaining a regular expression describing the behavior of a sequential circuit directly from its state diagram.Abstract:
This paper considers the application of signal flow graph techniques to the problem of characterizing sequential circuits by regular expressions. It is shown that the methods of signal flow graph theory, with the proper interpretation, apply to state diagrams of sequential circuits. The use of these methods leads to a simple algorithm for obtaining a regular expression describing the behavior of a sequential circuit directly from its state diagram.read more
Citations
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Journal ArticleDOI
Derivatives of Regular Expressions
TL;DR: In this paper the notion of a derivative of a regular expression is introduced atld the properties of derivatives are discussed and this leads, in a very natural way, to the construction of a state diagram from a regularexpression containing any number of logical operators.
Journal ArticleDOI
Probabilistic reachability for parametric Markov models
TL;DR: It turns out that the bottleneck lies in the growth of the regular expression relative to the number of states (nΘ(log n), so the approach is to arrive at an effective method that avoids this blow up in most practical cases.
Journal ArticleDOI
Ambiguity in Graphs and Expressions
TL;DR: The flow-graph technique for constructing an expression is shown to preserve ambiguities of the graph, and thus, if the graph is that of a deterministic automaton, the expression is unambiguous.
Book ChapterDOI
Probabilistic Reachability for Parametric Markov Models
TL;DR: It turns out that the bottleneck lies in the growth of the regular expression relative to the number of states (n *** (logn )), so a new approach is needed to arrive at an effective method that avoids this blow up in most practical cases.
References
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Journal ArticleDOI
A method for synthesizing sequential circuits
TL;DR: A new method of synthesis is developed which emphasizes formal procedures rather than the more familiar intuitive ones, and familiarity is assumed with the use of switching algebra in the synthesis of combinational circuits.
Journal ArticleDOI
Feedback Theory-Some Properties of Signal Flow Graphs
TL;DR: A study of the topological properties of such graphs leads to techniques which have proven useful, both for the discussion of the general theory of feedback and for the solution of practical analysis problems.
Journal ArticleDOI
Feedback Theory-Further Properties of Signal Flow Graphs
TL;DR: A way to enhance writing gain at a glance as discussed by the authors is to use the phrase "pray not frustrative" as a way to describe the goal of a sentence in a paragraph.
Journal ArticleDOI
Regular Expressions and State Graphs for Automata
Robert McNaughton,Hisao Yamada +1 more
TL;DR: Algorithms are presented for converting a state graph describing thebehavior of an automaton to a regular expression describing the behavior of the same automaton, and for converting an regular expression into a stategraph.