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1. Simulate a TM with infinite tape on both ends using a two-track TM with finite storage
2. Prove the following language is non-Turing recognizable using the diagnolization principle { (M, w) | TM M, starts with input w, does not halt}
3. Construct a TM for L = {w| w contains equal number of 0's and 1's} over {0,1} a) provide an algorithmic description b) draw the transition diagram
4. Consider a language L = {0m10n10max(m,n)| m, n>= 0}. Construct a TM that decides the language. Describe the algorithm and draw the transition diagram of the TM.
5. Given the following TM M, does M a) accept or b) reject on inputs w1 = 000 and w2=0000? Show the content of the input tape and positions of the head step-by-step.
The objective of the remainder of this assignment is to get you thinking about the problem of recognizing strings given various restrictions to your model of computation. We will w
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Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
When we say "solved algorithmically" we are not asking about a speci?c programming language, in fact one of the theorems in computability is that essentially all reasonable program
Computer has a single LIFO stack containing ?xed precision unsigned integers (so each integer is subject to over?ow problems) but which has unbounded depth (so the stack itself nev
S-->AAA|B A-->aA|B B-->epsilon
De?nition Deterministic Finite State Automaton: For any state set Q and alphabet Σ, both ?nite, a ?nite state automaton (FSA) over Q and Σ is a ?ve-tuple (Q,Σ, T, q 0 , F), w
Our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which aren't. The view of SL2 automata as generators le
While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless
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