Recursion is a natural use for a (stack or queue)

When determining the classification of data, which one of the following is the most important consideration? a. processing systemb. valuec. storage mediad. accessibility

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.

The instruction ishl (shift left integer) exists in jvm but not in ijvm. it uses the top two values on the stack, replacing the two with a single value, the result. the sec- ond-from-top word of the stack is the operand to be shifted. its content is shifted left by a value between 0 and 31, inclusive, depending on the value of the 5 least signifi- cant bits of the top word on the stack (the other 27 bits of the top word are ignored). zeros are shifted in from the right for as many bits as the shift count. the opcode for ishl is 120 (0x78).a. what is the arithmetic operation equivalent to shifting left with a count of 2? b. extend the microcode to include this instruction as a part of ijv.