finite-automata,automata,pda,pushdown-automaton,automata-theory

Of course, every state can be final in a deterministic pushdown automaton. Your approach seems correct to me. Depending on your definition on determinism it might be necessary to also add a transition that deals with the case where you read a 0 in state q_1 in order to have...

First, try to imagine the states your automaton can be in. Something like: Off, Ready, Working Afterwards imagine the buttons or inputs you have to perform to switch between these states. Do not forget to define every input on every state. If you leave out several transitions, the automaton is...

functional-programming,finite-automata,imperative-programming

About the same time as Turing Machines where developed (I'm just guessing that you are referring to TMs, when you say Automata theory is the basis for computers) also the lambda-calculus was suggested as a model of computation (okay not quite computers, but close). Both notions turned out to be...

Regarding your first question, on the runtime of the non-optimal DFA. Purely theoretically your intuition that it should still run in O(n) is correct. However, imagine (as an example) the following pseudo-code for the Kleene-Star operator: // given that the kleene-star operator starts at i=something while string[i] == 'r': accepting...

You can use the law of distributivity: (1*0)+(1*0(0+1)*(0+1)) = (1*0ε)+(1*0(0+1)*(0+1)) = (1*0)(ε+(0+1)*(0+1)) and then apply the definition of the the Kleene star a* = ε+a*a: = (1*0)((0+1)*) = 1*0(0+1)* ...

Instead of regular expressions I'd suggest you to use attoparsec. It's fast, robust and allows incremental input: A fast parser combinator library, aimed particularly at dealing efficiently with network protocols and complicated text/binary file formats. Regular expressions get ugly easily and in particular in Haskell, using a typed combinator parsing...

The next variable references a 2-dimensional array containing the state transitions of the DFA. The array has three rows, one for each state in the DFA. The line below shows that the array members in a row are the next state for 'a' and 'b' respectively. state = next[state][input.charAt(i) -...

levenshtein-distance,finite-automata

Can someone explain me the idea and the basic functionality of a levenshtein automata in easy words? A deterministic finite automaton (DFA) is an alphabet (set of possible input characters) a set of states (just abstract objects with no special properties) a transition function (given any state and an...

regular-language,finite-automata,dfa,pumping-lemma

A perhaps easier way to proof this is first modifying the language. Since regular languages are closed under complement and the intersection with another regular expression. This means that you can proof L is not a regular language by proving complement(L) is not a regular language, because if L' is...

regex,finite-automata,automata

For this proof, you don't have to construct a DFA for L. Your premise is that L is regular, so you know that there exists a DFA for L. Choose any, and now you can construct a NFA for L', by running your L DFA parallel to a copy of...

lexical-analysis,finite-automata,deterministic,lexical-scanner

The task you have is a similar one posed to many undergraduate students in compiler courses every year in thousands of universities, and the notes you cite are good sample of the many sets of course notes available on the topic. The solution is the same as any software engineering...

regex,algorithm,finite-automata

Some derivation of Levenshtein distance comes to mind - possibly not the fastest algorithm, but it should be quick to implement. We can ignore ^ at the start and $ at the end - anywhere else is invalid. Then we construct a 2D grid where each row represents a unit...

finite-automata,automata,automata-theory

s -> Bx x -> Ay | By | Cy y -> Ay | By | Cy | A It is not too difficult to draw the finite automaton. The small letters are the states, the capital letters are the input symbols. State "s" is the start state. From there...

finite-automata,automata,turing-machines,automata-theory

You can use a stack. To begin with, suppose you took your Turing machine, and added to it another track. Clearly, it is is possible to use the additional track for the stack. However, a multitrack Turing machine is equivalent to a Turing machine, and there is a mechanical way...

c++,regex,algorithm,pattern-matching,finite-automata

Check the table (b). All the states you are talking about are marked as 0. So you go back to the beginning. In the image you would get a lot of edges back to 0 so they don't show them (for clarity).