Under Construction.
Topic | Comment | More | |
Computation | |||
Primitive Recursive Functions | Clones, closure, bounded search, coding, Ackermann function. | pdf 6up | |
LOOP Programs | Comparison to prec functions, levels 0, 1, 2. | pdf 6up | |
Register Machines | Universality and undecidability. | pdf 6up | |
Turing Machines | Universality and undecidability. | pdf 6up | pdf pdf |
Decidability | Decision algorithms, semidecidability. | pdf 6up | |
Fundamentals | Stages, indices, recursion theorem. | pdf 6up | |
Reductions | Turing, many-one, one-one reductions, degrees. | pdf 6up | |
Arithmetical Hierarchy | Projections and complements, definability theory. | pdf 6up | |
Intermediate Sets | Post's problem, intermediate re sets. | pdf 6up | |
Kolmogorov Complexity | Program size complexity, incompressibility, Omega. | pdf 6up | |
Hypercomputation | Generalized computability, Turing barrier. | pdf 6up | |
Deterministic Complexity | Tractable problems, deterministic complexity classes. | pdf 6up | |
Space Complexity | Polynomial space, logarithmic space. | pdf 6up | |
Cook-Levin | Polynomial time reductions, NP-completeness. | pdf 6up | |
Randomness | Block counting, von Mises, Per-Lof. | pdf 6up | |
Random Classes | Schwartz-Zippel, Solovey-Strassen, RP, BPP. | pdf 6up | |
Rewrite Systems | Rewrite systems, Thue systems, Post systems. | pdf 6up | |
Context-Free Grammars | Formal grammars, Thue-systems, Church-Rosser, Post tag systems. | pdf 6up | |
Parsing | Parsing context-free languages, CYK algorithm. | pdf 6up | |
Context-Sensitive Grammars | Linear bounded automata, Immerman-Szelepsenyi | pdf 6up | |
Finite State Machines | |||
Deterministic Machines | Transition systems, scan algorithms, state complexity. | pdf 6up | |
Nondeterministic Machines | Rabin-Scott determinization, products, pebble arguments. | pdf 6up | |
State Complexity | Transition monoids, blow-up, alternating automata. | pdf 6up | |
Minimization | Quotients and covers, Moore's and Brzozowski's algorithms. | pdf 6up | |
More Minimization | Partition refinement, Hopcroft's and Valmari-Lehtinen algorithm. | pdf 6up | pdf pdf |
Minimization and NFAs | Paige-Tarjan, minimizing NFAs, hardness. | pdf 6up | |
Regular Expressions | Kleene's theorem, Floyd-Warshall algorithm, Arden's lemma. | pdf 6up | |
String Matching | KMP, Aho-Corasick, Baeza-Yates-Gonnet, Rabin-Karp. | pdf 6up | |
Monadic Second-Order Logic | Buechi-Elgot theorem, Schuetzenberger's theorem. | pdf 6up | |
Omega Automata | Buechi, Muller and Rabin automata, conversion algorithms. | pdf 6up | |
Omega Determinization | McNaughton's theorem, Safra's algorithm. | pdf 6up | |
Automatic Sequences | Prouhet-Thue-Morse word, decimations and kernels. | pdf 6up | |
Invertible | Invertible Mealy machines, automata groups, orbit rationality. | pdf 6up | |
Elementary Cellular Automata | Automtic structures, model checking ECA. | pdf 6up | |
Logic | |||
Propositional Logic | Boolean functions, propositional formulae, normal forms. | pdf 6up | |
Satisfiability | DPLL, Resolution, Horn clauses. | pdf 6up | |
Boolean Algebra | Duality, partial orders, Stone representation. | pdf 6up | |
Boolean Functions | Clones, Post's theorem. | pdf 6up | |
Boolean Decision Diagrams | Minimial automata, if-then-else normal form, ROBDDs. | pdf 6up | |
Equational Logic | Equational reasoning, Birkhoff's theorem, Boolean algebras. | pdf 6up | |
First-Order Logic | Signatures, first-order structures, Tarski truth, computable structures. | pdf 6up | |
FO Theories | Elementary equivalence, Goedel completeness, Goedel incompleteness. | pdf 6up | |
Proof Theory | Derivations, proofs, proof assistants, provers. | pdf 6up | |
Peano Arithmetic | Axiomatizing arithmetic, induction, Tennenbaum's theorem. | pdf 6up | |
Model Checking | Verification, Kripke structures, CTL, LTL. | pdf 6up | |
Sets | |||
Set Theory | Zermelo-Fraenkel, Neumann-Bernays-Goedel, Banach-Tarski. | pdf 6up | |
Cardinality | Cantor-Schroeder-Bernstein theorem, continuum hypothesis. | pdf 6up | |
Relations | Properties, orders, equivalence relations, composition. | pdf 6up | |
Functions | Types, kernels, closures, fixed points. | pdf 6up | |
Hash Functions | Universal hashing, perfect hashing. | ||
Ordinals | von Neumann ordinals, well-orderings, transfinite induction. | pdf 6up | |
Combinatorics | |||
Induction | IND, LEP, well-orders, recursive datatypes, recursive functions. | pdf 6up | |
Recursion | Sierpinski graphs, Hanoi transducer, Lucas theorem. | pdf 6up | |
Iteration | Orbits and fixed points, Floyd's trick, Goodstein sequences. | pdf 6up | |
Iteration | Ducci sequences, Pollard's rho method, Collatz problem. | pdf 6up | |
Iteration | Mandelbrot, decidability, Knaster-Tarski. | pdf 6up | |
Combinatorics | Combinations, permutations, binomials, ranking. | pdf 6up | |
Enumerations | Semigroup actions, enumeration, ranking, unranking. | pdf 6up | |
Fibonacci | Recurrence equations, Fibonacci numbers, Fibonacci field. | pdf 6up | |
Inclusion/Exclusion | Pigeon Hole Principle, Erdos-Szekeres, integer solutions. | pdf 6up | |
Moebius | Necklaces, bracelets, Lyndon words, Moebius inversion. | pdf 6up | |
Generating Functions | Polynomials, power series, growth functions. | pdf 6up | |
Algebra | |||
Number Theory | Euclidean algorithm, Chinese remainder, Wilson, Fermat. | pdf 6up | |
Number Theory | Groups, Cayley tables, Fibonacci monoid, SLPs. | pdf 6up | |
Groups | Abelian, symmetric, dihedral, normal subgroups. | pdf 6up | |
Groups | Group presentations, Cayley graphs, Novikov-Boone-Britton. | pdf 6up | |
Actions | Polya counting, Burnside's lemma. | pdf 6up | |
Polya-Redfield | Cycle index polynomials, pattern inventory, lamplighter group. | pdf 6up | |
Semi-Rings | Rings, polynomial rings, Schwartz's method. | pdf 6up | |
Polynomials | Evaluation, interpolation, roots, Schwartz's method. | pdf 6up | |
Finite Fields | Integral domains, irreducible polynomials, primitive elements. | pdf 6up | |
FF Applications | Montgomery reduction, linear feedback shift registers, AES Rijndael. | pdf 6up | |
FF Codes | Shannon, linear codes, syndrome, Hamming codes. | pdf 6up | |
Feedback Shift Registers | GPS, Fibonacci, Galois feedback shift registers, feedback polynomial. | pdf 6up | |
Miscellany | |||
Symbolic Dynamics | Sofic systems, one-dimensional cellular automata. | pdf 6up | |
Ehrenfeucht-Mycielsky | Non-learning, disjunctiveness, balance. | pdf pdf | |
Sigma Automata | Additive cellular automata, Fibonacci polynomials. | pdf 6up |