Automata, Computability and Complexity: Theory & Applications

Simulators and Graphical Interfaces for Finite State Machines
There exist many tools for working with FSMs. I’ve listed some of the ones I like best.

Finite State Transducers

  1. For phonetic string matching, including the Soundex system
  2. Roman numerals
  3. UPCs
    1. How UPCs work
    2. Barcode Magic, a barcode-creating applet

Transition-Network Tools for Software Engineering

  1. Simulink

Markov Models

  1. MARCA_Models software for creating and running various kinds of Markov models
  2. A simple example with a population of patients with diabetes
  3. Google’s PageRank algorithm
    1. The PageRank algorithm explained
    2. Cleve Moler’s article, which describes PageRank as a Markov model
    3. Training algorithms for efficient updating of the probabilities of huge Markov models such as PageRank
      1. Lee, Chris Pan-Chi, Gene H. Golub and Stefanos A. Zenios, 2003. “A fast two-stage algorithm for computing page rank”
      2. Langville, Amy N. and Carl D. Meyer, “Updating Markov chains with an eye on Google’s PageRank”, SIMAX (Siam Journal on Matrix Analysis and Applications) 27(4), pp. 968-987.
      3. Ipsen, Ilse C. F. and Steve Kirkland, 2006. “Convergence analysis of a PageRank updating algorithm”, SIMAX (Siam Journal on Matrix Analysis and Applications) 27(4), pp. 952-967.
  4. Markov models for music
  5. Markov models generating web pages
  6. OCR
    1. Wikipedia’s entry
    2. Public domain OCR resources
  7. Can English be described with a Markov model?
  8. Seminal paper by Claude Shannon
  9. A description from Programming Pearls, including links to Bentley’s Markov model generating programs
  10. The beetleinabox site, which includes an applet for creating Markov models of English
  11. A comprehensive list of web sites related to computer-generated text
  12. DadaDodo, a program that builds Markov models of texts and uses them to generate new texts. Its slogan is, “Eliminate all rational thought”. You can run a demo.

Hidden Markov Models (HMMs)

  1. Introductions to HMMs and the algorithms they use
  2. HMMs in speech and natural language processing, including spam filtering
  3. HMMs in computational biology
  4. HMMs in music

Büchi Automata and Other Automata on Infinite Strings

  1. Determinization of Büchi automata, which proves the nonequivalence of nondeterministic and deterministic Büchi automata and contrasts that with the equivalence of the two mnodels for Rabin and Muller automata