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Here is our algebra page. In earlier class sections I defined monoids, the two sided equivalence relation for a language, the syntactic monoid, aperiodic monoids,...
Here is a nice new page to describe automata theory results. In class on 27 Feb we mentioned Buchi`s Theorem (proved at the link), that a language is regular iff...
Buchi`s Theorem A language is definable in second order monadic logic if and only if it is regular. Proof Regular Second order monadic Let L be a regular language...
At the end of the regular 401 class we will talk about circuit complexity, the study of the resources needed to decide a formal language with a circuit family. If...
Descriptive complexity is the study of the relative difficulty of formal languages based on the syntactic resources needed to create logical formulas defining them...
A monoid is a set with an operation that is associative and has an identity element. Any finite monoid can be represented as a set of functions from a finite set to...
Parikh`s Theorem is a result in formal language theory that will occupy us for much of the 2013 H401 seminar. Let A be a nonempty alphabet with d letters. The Parikh...
Let M be a finite monoid . A program over M is a sequence of instructions (i, x, y) where i is a number in {1,..,n} and x and y are elements of M. The program computes...
A linear set is any set of the form a span (b1,..., bk). Here the plus sign means set addition: X Y {a b: a in X and b in Y}. The span of a set S is the set...
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Computer Science H401 Honors Colloquium for CMPSCI 401 Wiki This wiki was started by the instructor and students of CMPSCI H401 in Spring 2012. It contains material...
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