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

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?

## 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:

• 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

## Deterministic finite automata

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.

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

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?

## 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?

## Maximum characters in a deterministic Turing machine

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?

## I need help in creating deterministic finite automata

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.

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

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 ?

## Non deterministic finite automata

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.

## Deterministic Finite Automata

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.