Question: Prove that there is a language A {0, 1} with the following properties: (a) ForallxA,|x|4. (b) No regex of length at most 10 recognizes A.

Prove that there is a language A {0, 1} with the following properties: (a) ForallxA,|x|4.

(b) No regex of length at most 10 recognizes A.

Assume that the only allowed symbols in a regex are ( ) * + | 0 1

For example, the regex (0|1)*0110 has length 10.

Hint: You dont have to define A explicitly; just show that it has to exist. Count the number of languages satisfying (4a) and the number of Regex satisfying (4b), and then use the pigeonhole principle. To count the number of languages satisfying (4a), think about writing down all the strings of length at most 4, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. How many ways are there to make these choices?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

IBS is a global provider of point-of-sale systems and related services that enable businesses to accept electronic payments. As a new hire in the company's international headquarters' accounting...

Problem 1. Let {} (recall that = ). Prove that there is a DFA M having n accepting states that accepts L. (Assume an underlying alphabet of = {1}.) Then prove that L cannot be accepted by any DFA...

4. The length of a regex is the number of symbols in it (counting both special symbols such as and alphabet symbols such as 0; for instance, the length of (0|1)*0110 is 10. Show that there is a...

Let A = {0^n | n is prime}.(A is not DFA-recognizable.) Show that A* is DFA-recognizable. 3. Show that there is a language A {0, 1} with the following properties: (a) For all x A, |x| 5. (b) No DFA...

Theory of Computation Prove that there is a language A C 10,1) with the following properties: (a) For all x e A, 111 4. (b) No regek of length at most 10 recognizes A Assume that the only allowed...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

How many bracketings of length 2n will there now be? 1 [TURN OVER CST.93.2.2 2 Two teams A and B play a match in which the winner is the first team to win n games. If A needs i games to win and B...

(a) In SystemVerilog, what is the difference between: (i) The ternary operator ? and if...then...else statements? [2 marks] (ii) always_ff and always_comb? [2 marks] (iii) Blocking, non-blocking and...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

3.Show that there is a language A {0,1} with the following properties: (a) For all x A, |x| 5. (b) No DFA with fewer than 9 states recognizes A. 4. The length of a regex is the number of symbols in...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

A frictionless pistoncylinder device initially contains air at 200 kPa and 0.2 m3. At this state, a linear spring (F = x) is touching the piston but exerts no force on it. The air is now heated to a...

Demonstrate your knowledge of palladium cross-coupling reactions by suggesting structures for compounds (14) and (15). Suggest reagent(s) that would facilitate the cross-coupling reaction between...

if a firms projects differ in risk then one way of handeling this problem is to evaluate each project with the appropriate risk adjusted discount rate

1 3 . In temperature swing adsorption ( TSA ) , what triggers the desorption process? - A . Increasing pressure - B . Decreasing pressure - C . Increasing temperature - D . Decreasing temperature

The chapter notes that the rise in the U.S. trade deficit during the 1980s was due largely to the rise in the U.S. budget deficit. On the other hand, the popular press sometimes claims that the...

In 1998, the Russian government defaulted on its debt payments, leading investors worldwide to raise their preference for U.S. government bonds, which are considered very safe. What effect do you...

A case study in the chapter analyzed purchasing-power parity for several countries using the price of Big Macs. Here are data for a few more countries: Predicted Country Big Mac Rate Rate Indonesia...