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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.
Rubber shortnote
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
Let L 3 = {a i bc j | i, j ≥ 0}. Give a strictly 2-local automaton that recognizes L 3 . Use the construction of the proof to extend the automaton to one that recognizes L 3 . Gi
how to convert a grammar into GNF
Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(
Our DFAs are required to have exactly one edge incident from each state for each input symbol so there is a unique next state for every current state and input symbol. Thus, the ne
We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
short application for MISD
what is theory of computtion
When an FSA is deterministic the set of triples encoding its edges represents a relation that is functional in its ?rst and third components: for every q and σ there is exactly one
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