Definition: A σ-automorphism of a σ-structure A is just a σ-isomorphism h : A → A. The identity map idA is a σ-automorphism of A, but there are typically many other σ-automorphisms. A σ-structure is called rigid if it has no σ-automorphisms other than the identity. Show that the structures N := (ℕ,0, S,+,·) and Q := (ℚ,0,1,+,·) are rigid. Here, the symbol S is interpreted as the successor operation n ↦ n + 1 and all other symbols are with their standard interpretations.

Use the Pumping Lemma to show that the the following language over {a,b,c}* is not CF  {wct | t ∈ {a,b}* ∧ w is a substring of t}

Which is the best definition for lambda expression? the Church-Turing thesis X a function with some of its arguments curried an arithmetic expression with more than one side effect a function that has no name

Not handwritten Given the language L denoted by r = (a+b)* . (aa*+b) and, ∑ = {a,b} and ∏ = {c,d,x} h(b) = xd, h(a) = cdx please provide the homomorphic image of the regular expression h(r)

Closure Properties of Regular Languages 1. **Show that if a language family is closed under union and complementation, it must also be closed under intersection

24. Show that the grammars and are not equivalent. S→ aSbbSa|SS|a SaSbbSala

Draw a flow chart for one pass 1 of two-pass linking loader taking into consideration the automatic library search

Let Σ={a,b}. For each of the following languages over Σ, prove that the language is regular (a)  La​={w∈Σ∗:n0​(w)is divisible by 4 andwends in aab}

Discrete Structure

Determine if the following functions are homomorphisms / embeddings / isomorphisms. You must only answer: "not a homomorphism", "homomorphism buffnot an embedding", "embedding but not an isomorphism", "isomorphism".  If not specified, the interpretations of the symbols in the signatures are the standard ones.  a. n ↦ -n from (ℤ, 0, +) to (ℤ, 0, +).  b. n ↦ n from (ℕ+, ≤) to A := (ℕ+, ≤A), where ≤A is the divisibility relation, i.e. n ≤A m exactly when n divides m.  c. n ↦ n from A := (ℕ+, ≤A) to (ℕ+, ≤), where ≤A is the divisibility relation, i.e. n ≤A m exactly when n divides m.