Suppose we are given a sequence of medical tests, conducted after giving a medicine and representing infection values v1, v2 . . . vn. To evaluate the effectiveness of the medicine, the doctor wants to detect a falling trend. A trend is a subsequence of values at time instances i1 < i2 < ... < ik. Devise an algorithm to find the longest positive falling trend, i. e. the longest sequence of values vi1 vi2 . . . vij such thatvir ≥vir+1 +1andir

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, 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? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

Step 1: choose your topics review the project milestone reflections you submitted for modules 1 through 4. choose the one major idea or concept from each module that you feel most applies to your life. in addition, choose an important concept from module 5 that applies to your life. step 2: write your guidebook for each module: write a catchy headline that clearly and concisely sums up your chosen idea or concept write a brief explanation that includes a description of the concept, why it is important, and how it can be applied to your life to make a positive impact choose an exciting, powerful, or engaging image that illustrates your concept remember, you are writing one for each module, so you will have a total of five headlines, five descriptions, and five images. step 3: design your guidebook choose a format to present your digital guidebook. there are many 21st century tools available for creating and submitting your work in the online environment. for more information on tools your school uses, contact your instructor or visit the web 2.0 tools area.

Which requirement is an appropriate reason for a business to use it tools