CS 220 Winter 2011, Assignment 3, Due: February 171. Show that the functionf(x, y) =x*ycannot be computed by anyL1-program.2. Consider a programming languageQwhose only non-I/O instructions are of the forms:x←0,x←1,x←x+y,x←x-y(monus),do x ... end. Denote byQithe set of all programs withdo-loop depthi. Show that a function is computable by aG-program with running time boundedby an elementary function if and only if it is computable by aQ1-program.3. Show that fori≥1, a function is computable by aQi-program if and only if it is computable byanLi+1-program.4. From the definition of partial recursive functions, show that every partial recursive function canbe computed by aGprogram.5. Consider a DFA (deterministic finite automaton)Moperating on the upper-right quadrant ofthe plane, filled withλ’s, with the boundaries delimited by $’s.Mstarts in its intital state onthe $ in the cell at the origin (location (0,0)).Mhas a finite number of states and can only readand not write. Note thatMhas now four directions of moves. Show that the halting problemfor such DFAs is undecidable.
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