Technique for constructing a dfsm

Assignment Help Theory of Computation
Reference no: EM131577703

Qusetion: We introduce a technique for constructing a deterministic finite-state machine(DFSM) equivalent to a given deterministic finite-state machine with the least number of states possible. Suppose that M = (S, I, f, s0,F) is a finitestate automaton and that k is a nonnegative integer. Let Rk be the relation on the set S of states of M such that sRkt if and only if for every input string x with l(x) ≤ k [where l(x)is the length of x, as usual], f (s, x) and f (t, x) are both final states or both not final states. Furthermore, let R∗ be the relation on the set of states of M such that sR∗t if and only if for every input string x, regardless of length, f(s, x) and f(t, x) are both final states or both not final states

a) Show that for every nonnegative integer k, Rk is an equivalence relation on S. We say that two states s and t are k-equivalent if sRkt.

b) Show that R∗ is an equivalence relation on S. We say that two states s and t are *-equivalent if sR∗t.

c) Show that if s and t are two k-equivalent states of M, where k is a positive integer, then s and k are also (k - 1)-equivalent

d) Show that the equivalence classes of Rk are a refinement of the equivalence classes of Rk-1 if k is a positive integer.

e) Show that if s and t are k-equivalent for every nonnegative integer k, then they are ∗-equivalent.

f ) Show that all states in a given R∗-equivalence class are final states or all are not final states.

g) Show that if s and t are R∗-equivalent, then f (s, a) and f (t, a) are also R∗-equivalent for all a ∈ I.

Reference no: EM131577703

Questions Cloud

What do you see as the greatest challenges to recovery : What do you see as the greatest challenges to recovery in this instance? What are the greatest opportunities that exist as a result of the disaster?
Express each of the given sets using a regular expression : Express each of these sets using a regular expression. The set of strings of one or more 0s followed by a 1.
Describe the structure of your ecosystem : Describe the structure of your ecosystem including important abiotic features and dominant plant and animal species.
What are three examples that the driver could do : The effect of combining tasks - what are three examples that the driver could do to combine tasks to improve efficiency?
Technique for constructing a dfsm : We introduce a technique for constructing a deterministic finite-state machine(DFSM) equivalent to a given deterministic finite-state machine.
What fee should they charge to obtain contribution margin : What fee should they charge to obtain a contribution margin of 35%? What is the target fee for an overnight stay?
What amount should be reported for pension expense : Question - Presented below is information related to Marley Inc. pension data for 2008. What amount should be reported for pension expense in 2008
Calculate the direct materials ending inventory : Problem - Moody Blues Chocolate Factory uses job costing to cost its products. Calculate the direct materials ending inventory
Listening and openness issue : With any new system, some problems are going to be solved because they are going to be automatized, but if the listening and openness issue.

Reviews

Write a Review

Theory of Computation Questions & Answers

  Finite-state machine design

Create a finite-state machine design to turn your FPGA development board into a simple programmable music box.

  Redundant sequence identi cation

Redundant sequence identi cation

  Compute a shortest superstring

Dynamic programming algorithm to compute a shortest superstring.

  Propositional and predicate logic

Write down a structural induction principle for the PlayTree free type

  Design a syntactic analyzer

Design a syntactic analyzer for the language specified by the grammar

  Design unambiguous grammar to parse expressions

Write a program would read two numbers and then print all numbers between the first and the second, inclusive. Design unambiguous grammar to parse expressions

  Consider a logic function with three outputs

Consider a logic function with three outputs,  A ,  B , and  C , and three inputs,  D ,  E , and  F . The function is defined as follows:  A  is true if at least one input is true,  B  is true

  Considering a single programmed operating system

Considering a single programmed operating system, what is the minimal total time required to complete executions of the two processes? You should explain your answer with a diagram.

  How to construct an nfa

Give a construction that assumes you are given a DFA for L and show how to construct an NFA (with or without ε-moves) to recognize sort(L).

  Equivalence classes to construct minimal dfa for language

How many equivalence classes does this relation have and what are they? Use these equivalence classes to construct the minimal DFA for the language.

  Impact of moore-s law on data center costs

Discuss the impact of Moore's law on data center costs on such things as servers and communications equipment. List at least 3 steps or recommendations your data center can take to offset some or all of the effect of Moore's law.

  Problem encountered in statements in predicate logic

How the problem would be encountered in attempting to represent the following statements in Predicate logic. it should be possible to: John only likes to see French movies.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd