Select the Context Free Grammar below that is in the form of Chomsky Normal Form. G=( {S,a,b}, {0,1}, S, {S0b|1a, a0|OS|1aa, b➡1|1s|Obb}) ☐ G=( {S,a,b}, {0,1}, S, {Sab|1, a0|1|Sa, b→1|bs}) ☐ G=( {S,A,B}, {a,b}, S, {S AB|bA, Aa|b|SB, B→a|SB}) ☐ G=( {S,A,B}, {a,b}, S, {S-BB|b, A➡a|b|SS, B→a|SA})
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- question Compute the homology groups of the space S 1 ∨ S 1 ∨ S 2 (the wedge sum of the circle, circle, and sphere) in all dimensions using the reduced homology. Please write on paper and upload it. The answer is you get Z when n = 0, 2, ZxZ when n = 1, and 0 when n is 3 or greater. Write the computation in detail. Please answer it if you know homology theory or singular homology and how to use the chain complex sequences. Write it on paper with the long exact sequence..Answer the given question with a proper explanation and step-by-step solution. Data Structures - Order functions from slowest to fastest 3n, 2n, 5n2 + 2n - 2, n log n, log(n2), 100n + n log n, 2n3Build a CFG to show that L= bnamb3n (m,n>=1) is context free.
- A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Comment on the results from the graph and determine the value of the time when the waves are with the same phase and assemble constructively and the time when they are with phase of opposite and interfere destructively. Doing the corresponding numerical simulations show what happens with the increase of the difference between the frequencies of the two waves and vice versa.Give a state transition diagram of a DFA that recognizes the following language over the alphabet{0,1}): The set of all strings such that every occurrence of 1 is followed by at least two Os, e.g., 01000100100, 10010000001000000, 00001000 are in this language, but 001 is not. The set of all strings that does not contain pattern 0101. The set of all strings except 101 and 11. The set of all string such that every even position contains 0. For example, 00000,101,100010 are in this language, but 010 and 1101 are not.Hi, This part is about regular expressions (REs) and finite-state automata (FSAs). Notation: in the REs below, the Kleene star has higher precedence than sequencing; andsequencing has higher precedence than +. E.g. 10∗1 + 11∗1 = (1(0∗)1) + (1(1∗)1). Consider the regular expression r: (01 + 11)∗10 (1∗ + 0∗) 1.1) Which of the following words (ε is the empty word) belong to the language defined by r? Options: ε, 101, 001101, 111011, 111010 1.2) For each of your answers in Question 1.1, give a brief explanation. For example, you can explain how the regular expression will accept (i.e. match) the words that belong to its language, and how it will not accept those that do not belong in it. 1.3) Give, as a transition graph, an FSA (possibly with ε-transitions) recognising the same language as r.Note: You should not use transitions with composite labels, e.g. of the form q1 →42→ q2. Thanks for the help :)
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- Prove by Systematic Semantic Tableaux ∃xR(x,x)∨∃x[R(x,x)→¬∃yR(y,x)]In this problem, let REF(x.i) → DEF(x.k) denote that the linker willassociate an arbitrary reference to symbol x in module i to thedefinition of x in module k . For each example below, use thisnotation to indicate how the linker would resolve references to themultiply-defined symbol in each module. If there is a link-time error(rule 1), write " ERROR ". If the linker arbitrarily chooses one of thedefinitions (rule 3), write " UNKNOWN ".A./* Module 1 */ /* Module 2 */int main() static int main=1[{ int p2()} {}(a) REF(main.1) → DEF(_____._____)(b) REF(main.2) → DEF(_____._____)B./* Module 1 */ /* Module 2 */int x; double x;void main() int p2(){ {} }(a) REF(x.1) → DEF(_____._____)(b) REF(x.2) → DEF(_____._____)C./* Module 1 */ /* Module 2 */int x=1; double x=1.0;void main() int p2(){ {} }(a) REF(x.1) → DEF(_____._____)(b) REF(x.2) → DEF(_____._____)(a) Design a PDA P that recognizes the language L = {x#y : x, y ∈{1}∗∧ |x| > |y|} over the alphabet Σ = {1, #}. Draw a state diagram according to the format of the textbook and the slides,i.e., start with an empty stack. Furthermore, ensure that every move either pushes or pops, but not both.(b) Obviously, you can easily create a CFG for such a trivial language like L. Here, you are asked to not just produce any CFG for L, but follow the procedure PDA-to-CFG to obtain such a grammar. Even for such a simple PDA, the grammar would be a bit lengthy. Therefore, we make one modification. You don’t have to write any rules that involve variables that generate the empty language. Such rules would have no effect anyway.