Deterministic Finite Automata vs Java

You need to select a device controller. You have two options: Option 1: Implement with a DFA Option 2: Implement using Java The primary advantage of a DFA over a program written in Java is as follows:

Answer choices:

  • A DFA requires fewer computational resources
  • A DFA is faster than a program in Java
  • Running a DFA costs less than running a program written in Java
  • It doesn’t matter if we use a DFA or a program written in Java, as long as it gets the job done

Does all derivation trees generated by context free grammar in cnf form can be recognized by buttom up tree automata?

G is a context-free grammar in Chomsky normal form.

we define L(G) to the set of all derivation trees that formed by G.

Is it possible to create a non-deterministic bottom-up tree automaton that will accept L(G) exactly? if so, how to construct such automaton?

I think it’s true, so I’m trying to construct the automaton but having hard time to define specifically the transition function.

hope to get help.

Finding the upper bound of states in Minimal Deterministic Finite Automata

I have a task to determine the upper bound of states in the Minimal Deterministic Finite Automata that recognizes the language: $ L(A_1) \backslash L(A_2) $ , where $ A_1 $ is a Deterministic Finite Automata(DFA) with $ n$ states and $ A_2$ is Non-deterministic Finite Automata(NFA) with $ m$ states.

The way I am trying to solve the problem:

  1. $ L(A_1) \backslash L(A_2) = L(A_1) \cap L(\Sigma^* \backslash L(A_2)$ , which is language, that is recognised by automata $ L’$ with $ n*m$ states
  2. Determinization of $ L’$ which has $ (n*m)^2$ states and it is the upper bound of states.

Am I right?

Regular languages, automata

I want to ask about the definition of regular languages. My book says there has to exist a deterministic finite automaton that recognizes it. Does this mean the finite automaton recognizes exactly this language and nothing else or it can recognize possibly some other words not in the language?

How to define an automata for zig zag concatenation? [duplicate]

I have two DFAs one for language A and one for language B. I’m asked to make an FDA that is the zig-zag concatenation of letters of A and letters of B. This is described by the following: {w: w = $ a_1 b_1$ $ a_k b_k$ and $ a_1…a_k \in A$ and $ b_1 … b_k \in B$ }. With $ 1 \leq i \leq k$ and $ a_i \in \Sigma$ and $ b_i \in \Sigma$

This automata should be described as a 5-tuple {Q, $ \Sigma$ ,$ \delta$ ,$ q_0$ ,$ F$ }.

I simply do not know how I would go about defining the total function $ \delta$ .

This is what I tried:

$ Q = Q_A \cap Q_B$ // We only want the words that contains both a and b

$ F = F_A \cap F_B$ // The accepted states should contain both letter from a and from b.

$ q_0 = q_A$ //because the word starts with a letter from a.

$ \Sigma$ // in this problem we aren’t interested in defining the alphabet we just leave the symbol as is in the 5-tuple.

Finding a finite automata that accepts a language that is the combination of two other languages with their own automata

I’m told that we have two DFA one A and one B both on alphabet $ \sum$ .

I’m then told to define a DFA (5-tuple representation) with this condition {w | w = $ a_i b_i$ $ a_k b_k$ and all the $ a \in A$ and all the $ b \in B$ }

Also 1 $ \leq$ i $ \leq$ k and $ a_i \in \sum$ and $ b_i \in \sum$ .

However I simply do not understand how I’m supposed to do this. Simply put my confusion is what $ w = a_i b_i$ mean. Is it concatenation? Does it mean that the word $ w$ is the concatenation of a with b?

Why should an average programmer learn automata theory?

Good programming relies heavily on choosing an efficient algorithm for the task at hand and yet an average programmer hardly uses 50 pages worth of algorithms from the Cormen book in his/her career.

Recently I started reading some CS books, long after completing my bachelors degree. One of the books is the Theory of Computation by Micheal Sipser. Although I love the content and still am in the beginning chapters, I cannot imagine where I would use the information provided in this book in my job.

What is the use of Automata Theory in the industry?