If there is a finite set of Instances of size n and the set of (reasonable) deterministic algorithms is finit.

Can any randomized Algorithm be seen as a probability distribution over the set of deterministic Algorithms? And if yes, why?

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# Tag: deterministic

## Is any randomized Algorithm a probability distribution over the set of deterministic Algorithms?

## Deterministic Finite Automata vs Java

## Deterministic finite automata

## How to determine if a language produced by grammar is recognizable by deterministic pushdown automaton (DPDA)?

## Finding the upper bound of states in Minimal Deterministic Finite Automata

## Maximum characters in a deterministic Turing machine

## I need help in creating deterministic finite automata

## Usual distances on DFAs (Deterministic Finite Automata)?

## Non deterministic finite automata

## Deterministic Finite Automata

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If there is a finite set of Instances of size n and the set of (reasonable) deterministic algorithms is finit.

Can any randomized Algorithm be seen as a probability distribution over the set of deterministic Algorithms? And if yes, why?

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

For Sigma={a,b}, Design DFA for the language a) L={w:(na(w)+2nb(w))mod 3<2}. b) accepting set of string over {a,b} in which anbmcl, where n , m and l is greater than equal to 1.

I have a following grammar: S -> aSa | bSb | lambda.

And I have to figure out whether the language produced by this grammar is recognizable by DPDA. I can’t find any theoremas about it. Obviously, it’s a context-free language and can be recognized by DPA, but what about DPDA?

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:

- $ 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
- Determinization of $ L’$ which has $ (n*m)^2$ states and it is the upper bound of states.

Am I right?

Assume we have a deterministic Turing machine $ M = (q_s, q_a, q_r, \Sigma, \Gamma, \delta, Q, b)$ where $ q_s,q_a,q_r$ are the (unique) starting state, accept state and reject state respectively, $ Q$ the set of non-final states, $ \Sigma$ the input alphabet, $ \Gamma$ the tape alphabet, $ \delta$ the transition function and $ b \in \Gamma$ the blank symbol.

How many characters can fit in $ \Gamma$ , as a function of $ |\Sigma|, |Q|$ such that for each $ c \in \Gamma$ , $ \delta$ will be defined by it for some state and character?

Let Σ = {a, b, c}. Draw a DFA that rejects all words for which the last two letters match. Draw a DFA that rejects all words for which the first two letters match.

I’ve been searching in the literature for examples of **distances defined on the set of the DFAs (or on the set of minimal DFAs) that are defined on a given alphabet sigma**.

Since the languages they describe (regular languages) can potentially have an infinite size, defining a distance is not a trivial matter.

Nevertheless, having a distance on these objects can be useful, in order to fit these in metric spaces, which allows for a range of things (in my case to assess the performance of an algorithm).

My only consistent idea so far is to create a distance similar to the edit-distance in labeled graphs on the minimized DFAs.

Does someone have ever heard of other distances ?

I’m stucked trying to determine the NFA of this subset ({qo,q1},{1,0},{q0,0,q0},{q0,0q1},,{q0,1,q0},q0,{q1}). I’ll be glad if someone should help me tackle the problem.

I need to create a deterministic finite automata, that can be any length, and is made up of 0s and 1s. Among any subsequent 3 numbers, there needs to be exactly two 1s, and exactly one 0. I’ve spent a couple hours studying DFAs, but I can only find solutions like the one I need to one of these issues. Meaning that among the 3, there can be at most 1 of something, or there needs to be at least 2 of something. I’m pretty much lost in how I’m supposed to combine these into a single DFA. Any help would be appreciated.

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