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Consider the finite-state automaton AA given by the following transition diagram:
- Draw the transition diagram for A bar, the quotient automaton of A.
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- Exercises 7. Express each permutation in Exercise as a product of transpositions. 1. Express each permutation as a product of disjoint cycles and find the orbits of each permutation. a. b. c. d. e. f. g. h.Find the order of each permutation in Exercise 1. Express each permutation as a product of disjoint cycles and find the orbits of each permutation. a. [ 1234545312 ] b. [ 1234513254 ] c. [ 1234541352 ] d. [ 1234535241 ] e. [ 12345673456127 ] f. [ 12345675137264 ] g. [ 1234513452 ][ 1234532415 ] h. [ 1234523415 ][ 1234513542 ]For the finite state automaton given by the transition diagram in figure 1, find the states, the input symbols, the initial state, the accepting states and write the annotated next state table Figure 1 b -0 02 b 01 03 b b
- create an equation showing the symbol (notation) introduced for the theoretical autocovariance of order 2. include the two lines of R script required to install and load the fpp3 package (do this in a verbatim environment)Design a deterministic finite automaton that accepts all binary strings that correspond to a value divisible by 3. For example, it should accept 110 (since 6 is divisible by 3), but not 101 (since 5 is not divisible by 3).Human genetic material (DNA) is made up of sequences of the molecules adenosine (A), guanine (G), cytosine (C), and thymine (T), which are called bases. A codon is a sequence of three bases. Replicates are allowed, so AAA, CGC, and so forth are codons. Codons are important because each codon causes a different amino acid to be included in a protein. a. How many different codons are there? b. How many different codons are there in which all three bases are different? c. The bases A and G are called purines, while C and T are called pyrimidines. How many different codons are there in which the third base is a purine and the others are pyrimidines? d. What is the probability that all three bases are different? e. What is the probability that the third base is a purine and the others are pyrimidines?