Application Area

Theoretical Idea

Specific Problem(s)

Artificial intelligence

production rules

rule based systems,

expert systems,

cognitive modeling

undecidability

logical reasoning

complexity of search

logical reasoning,

game playing

lambda calculus

Lisp

Business rule modeling

production rules

model business practices

Computational biology

FSMs

sequence matching

HMMs

sequence matching

regular expressions

sequence matching

context-free grammars

protein and RNA folding

Lindenmayer systems

model growth and evolution

Dance

context-free grammars

describe dance steps

Databases

context-free grammars

query languages

normal forms

query languages

Games

complexity

puzzles and games

heuristic search: A*

Route finding

heuristic search: minimax

chess, Go

nondeterministic FSMs

Define NPCs in interactive games

rule-based systems

Define NPCs in interactive games

Graphics

context-free grammars

graphics metalanguages

Hardware design

FSMs

circuit design

Büchi automata

model checking for verification

decidability

model checking for verification

Internet

regular expressions

spam filtering,

pattern matching

context-free grammars

markup languages

decidability and complexity

Semantic Web

Manufacturing

complexity

routing

Markup languages

context-free languages

HTML, XML, RDF

Music

Markov models

composition

HMMs

composition

grammars

analysis of musical style,

composition

Lindenmayer systems

composition

Natural language processing

FSMs

morphological analysis

HMMs

part of speech tagging,

speech recognition

context-free grammars

parsing

feature/unification grammars

parsing

Networks

FSMs

network protocols

decidability

correctness of concurrent systems

complexity

modeling networks as graphs

Programming languages and compilers

FSMs

lexical analysis

context-free grammars

BNF for syntactic specification

context-free grammars

parsers for compilers

context-free languages

type checking isn't cf

undecidability

dead code elimination

undecidability

checking for loops

lambda calculus

functional programming

Security

FSMs

physical security systems

undecidability

correctness of security models,

virus detection

complexity

cryptography

Software engineering and programming

FSMs

statecharts for specifying systems,

prototyping,

test-case generation

island grammars

reverse engineering

decidability

model checking

undecidability

program verification,

checking for equivalence of programs

complexity

model checking

String searching

regular expressions

spam filtering,

text querying

Web searching

nondeterminism

asynchronous parallel search

decidability and complexity

Semantic Web