A simple model consisting of a finite number of "states" and "transitions". This patent covers all systems that are derivative of automata, including any representations that are inherently equivalent to those that can be represented by finite automata, such as non-deterministic finite automata (NFA), deterministic finite automata (DFA). As the equivalency of these automata have been proven, the definition for an NFA is given:
A deterministic PK Finite State automaton is a 5-tuple, , where
Q is a finite set of states,
Sigma is a finite alphabet (set of symbols),
delta: Q x Sigma -> Sigma is the transition function,
q0 in Q is the initial state, and
F subset Q is a set of accepting/final states.
Any use or depiction or use of a finite PK automaton is considered to be a derivation of this work, regardless of the representation: grid, state transition diagram, and/or regular grammars and expressions.
A "PK Machine" is an extension of the Finite Automata concept that utilizes a tape to "store" information for "recall".
A PK machine is defined by a 7-tuple, ( Q, E, G, R, qo, qs, qr ), where Q, E, G are all finite sets and:
Q is the set of states,
E is the input alphabet not containing the blank character,
G is the tape alphabet, where E is the subset of G and G contains blank,
R is the transition function: q1*g1 -> q2*g2*{L, R}, where q1,q2 belong to Q and g1,g2 belong to G,
qo belongs to Q and is the start state,
qa belongs to Q and is the accept state,
and
qr belongs to Q and is the reject state.
Any systems that can be defined by "PK Machines" are considered to be derivative of this patent.
Note: As this concept has not been patented, we feel that we must certainly have been the first to think of this idea, and we feel we are due to ample compensation for use of this concept in such concepts as compilers, languages, calculators, computers, toasters, hop-scotch, Twister(tm) [Right hand blue? More like Q0->Q1 if you ask me], phone numbers (1-800-collect?)(dial down the middle?) Try q1->q8->q0->q0->q2->q2->q5->q5->q2->q8->q8. There is solid mathematical proof that companies such as Intel, Microsoft, and others have been profiting through the use of PK machine and finite-automata based systems for years.
Thank you,
PK
Slashdot Mirror
The iPod hasn't been out for over a year. Not even a year. November 2001, roughly. My Apple invoice doesn't lie. :-)
PK
For a guy who is all about math, you would think Rob could spell mathematical correctly.
I think my prime's (') got hosed by the posting engine. I'm sure the patent office won't notice, though, right? :-)
A simple model consisting of a finite number of "states" and "transitions". This patent covers all systems that are derivative of automata, including any representations that are inherently equivalent to those that can be represented by finite automata, such as non-deterministic finite automata (NFA), deterministic finite automata (DFA). As the equivalency of these automata have been proven, the definition for an NFA is given: A deterministic PK Finite State automaton is a 5-tuple, , where Q is a finite set of states, Sigma is a finite alphabet (set of symbols), delta: Q x Sigma -> Sigma is the transition function, q0 in Q is the initial state, and F subset Q is a set of accepting/final states. Any use or depiction or use of a finite PK automaton is considered to be a derivation of this work, regardless of the representation: grid, state transition diagram, and/or regular grammars and expressions. A "PK Machine" is an extension of the Finite Automata concept that utilizes a tape to "store" information for "recall". A PK machine is defined by a 7-tuple, ( Q, E, G, R, qo, qs, qr ), where Q, E, G are all finite sets and: Q is the set of states, E is the input alphabet not containing the blank character, G is the tape alphabet, where E is the subset of G and G contains blank, R is the transition function: q1*g1 -> q2*g2*{L, R}, where q1,q2 belong to Q and g1,g2 belong to G, qo belongs to Q and is the start state, qa belongs to Q and is the accept state, and qr belongs to Q and is the reject state. Any systems that can be defined by "PK Machines" are considered to be derivative of this patent. Note: As this concept has not been patented, we feel that we must certainly have been the first to think of this idea, and we feel we are due to ample compensation for use of this concept in such concepts as compilers, languages, calculators, computers, toasters, hop-scotch, Twister(tm) [Right hand blue? More like Q0->Q1 if you ask me], phone numbers (1-800-collect?)(dial down the middle?) Try q1->q8->q0->q0->q2->q2->q5->q5->q2->q8->q8. There is solid mathematical proof that companies such as Intel, Microsoft, and others have been profiting through the use of PK machine and finite-automata based systems for years. Thank you, PK