Question 2 (10 pt): In this question we look at an extension to DFAs. A composable-reset DFA (CR-DFA) is a five-tuple, (Q,S,d,q0,F) where:
– Q is the set of states,
– S is the alphabet,
– d:Q×(S?{?})?Qisthetransitionfunction, – q0 ? Q is the start state, and
– F ? Q is the set of accept states.
Every CR-DFA must satisfy one additional property:
When running a CR-DFA one can take a ?-transition if and only if the input has already been exhausted, and d cannot have any cycles that have a ?-transition.
A CR-DFA differs from a DFA by the addition of a new symbol denoted ? which can only be used by the transition function. This symbol is not part of the alphabet of the DFA.
The run function for a CR-DFA is defined as follows:
dˆ 0 : Q × S * × S * ? Q dˆ0(q,e,w1) = q
if d(q, ?) is undefined. dˆ0(q, e, w1) = dˆ0(q', w1, w1)
if d(q, ?) = q'
dˆ0(q, aw, w1) = dˆ0(q', w, w1)
if d(q, a) = q' dˆ : Q × S * ? Q
dˆ ( q , w ) = dˆ ( q , w , w ) 0
1
We can see that the run function, dˆ, is defined interms of an auxiliary function called dˆ0. The latter takes three arguments: i. the current state, the input word, and a second input word called w1. The second input word is called an accumulator, and it will be used to remember the original input to the run function, but when defining the auxiliary run function we leave this arbitrary.
The definition of the auxiliary run function follows the definition of the run function for DFAs, but in the case where the input word has been exhausted we check to see if the transition function allows the input to be reset to w1, and if it does, then we call dˆ0 on the next state given by d, and the input word is reset to w1. If when the input is exhausted and the transition function does not allow a ?-transition, then we proceed as usual.
Note that the definition of acceptance for a CR-DFA is the same as for DFAs.
We now define an interesting language. Suppose S = {a, b, c, d, ?, ?} is an alphabet. The symbol ? represents a binary operation, and the symbols a, b, c, d, and ? represent inputs to the binary operation ?. The language L is defined by the following:
i. a,b,c,d,? ? L
ii. Foranyei ?S,thewordw=e1?e2?e3?···?en ?L
iii. For any w ? L, any well-balanced parenthesization of w is a member of L
iv. There are no other words in L.
The following are some example words in L:
a
b
c
d
?
(a?b) (a?(b?c)) (a?(b?(c?d))) a?b?c (a?b)?c
So the words of L are all the possible associations of applications of the binary operation ?. Define a CR-DFA in the diagrammatic from used with DFAs that recognizes the language L as defined above. In addition, describe why CR-DFAs are bad in practice.

Posted Date: 2/2/2015 8:26:13 PM | Location : United States

Ask an Expert

Related Discussions:- A composable-reset DFA (CR-DFA) is a five-tuple, Assignment Help, Ask Question on A composable-reset DFA (CR-DFA) is a five-tuple, Get Answer, Expert's Help, A composable-reset DFA (CR-DFA) is a five-tuple Discussions

Write discussion on A composable-reset DFA (CR-DFA) is a five-tuple
Your posts are moderated

Write your message here..

Related Questions

Computations of sl automata, We will specify a computation of one of these ... We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea

Programming languages, Different types of applications and numerous program... Different types of applications and numerous programming languages have been developed to make easy the task of writing programs. The assortment of programming languages shows, dif

Pendulum Swings, how many pendulum swings will it take to walk across the c... how many pendulum swings will it take to walk across the classroom?

Hhhhhhhhhhhhhhhhh, Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh... Ask question #hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhMinimum 100 words accepted#

Alphabets - strings and representation, A finite, nonempty ordered set will... A finite, nonempty ordered set will be called an alphabet if its elements are symbols, or characters. A finite sequence of symbols from a given alphabet will be called a string ove

Pumping lemma constant, a) Let n be the pumping lemma constant. Then if L i... a) Let n be the pumping lemma constant. Then if L is regular, PL implies that s can be decomposed into xyz, |y| > 0, |xy| ≤n, such that xy i z is in L for all i ≥0. Since the le

Decision problems, In Exercise 9 you showed that the recognition problem an... In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems

Powerset construction, As de?ned the powerset construction builds a DFA wit... As de?ned the powerset construction builds a DFA with many states that can never be reached from Q′ 0 . Since they cannot be reached from Q′ 0 there is no path from Q′ 0 to a sta

Trees and graphs , Trees and Graphs Overview: The problems for this ... Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be

Bonds, . On July 1, 2010, Harris Co. issued 6,000 bonds at $1,000 each. The... . On July 1, 2010, Harris Co. issued 6,000 bonds at $1,000 each. The bonds paid interest semiannually at 5%. The bonds had a term of 20 years. At the time of issuance, the market r