# Hw10 - Homework 10 CISC 303 Timo Kötzing([email protected]

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 10 CISC 303 Timo Kötzing ([email protected]) Handed out: Monday, May 4. Due Date: Friday, May 8. Problem 1. (2 or 8 points) Let f : N 2 → N , ( x,y ) 7→ x + y ( f is addition on natural numbers). If you have showed that f is computable when all inputs are unary, show that f is also computable when the inputs are binary (8pts). If you have showed that f is computable when all inputs are binary, show that f is also computable when the inputs are unary (2pts). Problem 2. (8 points) Use the characterization given in Theorem 3.2.1 of the Lecture Notes to show that the following two functions are (total) computable. (i) g : N 2 → N , ( x,y ) 7→ x · y ; (ii) g 1 : N → N ,x 7→ x ! . 1 Problem 3. (8 points) (i) Prove informally that L = { code( M ) | M TM and M halts on ε in ≤ 1000 steps } is decidable. (ii) Prove informally that L = { code( G ) | G is ambiguous CFG } , the Ambiguity Problem for CFGs , is semi- decidable....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online