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.

Q: Prove that the following language A is decidable (e.g., give a TM that decides A). A = {⟨M⟩ | M is…

A: We will prove that language A = {⟨M⟩ | M is an NFA and L(M) = B}, where B is a regular language, is…

Q: Using Direct Proof, Show that if x an Integer then 2x^2 +6c+8 is even

A: Direct proof of p(x) => q(x) for all x belongs to D:   1) Assume p(x) is true for any arbitrary x…

Q: 2. Recall in lambda calculus, logic connectives NOT and OR can be defined as: NOT = (Ax | xFT) OR=…

A: Answer: I have given answered in the handwritten format in brief explanation.

Q: 4. What does the following Lisp function do? (defun myfun (1st) (cond ((null lst) ()) ((equal (car…

A: Defun can be used to define a new function, to install a corrected version of an incorrect…

Q: Give an unambiguous grammar for language L(G); using G defined below.

A: The derivation in a CFG can be represented using trees. Such trees representing derivations are…

Q: Let L be a first-order language and let A be an L -structure. If s is a variable assignment function…

A: Answer :

Q: For each of the following languages Ls {a, b}*, show that the elements of the infinite set {a"|n >…

A: Shown that the given language is pairwise distinguishable

Q: Consider the context free grammar G-(V.E.R.S), where fa.b}. V-la.b.S} R {S→aSb. S-aSa, SbSa, S-bSb,…

A: The context free grammar shown that regular

Q: Defined the following Clojure program that deals with primitive lambda logic representation: (ns…

A: The provided Clojure program deals with primitive lambda logic representation, defining basic…

Q: 1. Is the following set of connectives functionally complete? Explain. {→, 1}

A: Given: The truth function are {0,1} {→,⊥}

Q: Take the polymorphic type for example: (c, h) -> (c -> h) -> (h, h) Make a list of all conceivable…

A: Answer has been explained below:-

Q: Eliminate all lambda productions, unit productions, and useless productions from the following…

A: Eliminate lambda productions, unit productions, and useless productions from the given grammar is…

Q: push down automata for L= {axbycm such that y - m = x}

A: The states in the PDA are : Start State: A Final State: B, C,D,E Intermediate State: F

Q: algorithm for finding all occurrences of a sequence P common to two sequences S1 and S2 using the…

A: algorithm for finding all occurrences of a sequence P common to two sequences S1 and S2 using the…

Q: If a function f from A to B is bijection, i.e. it is both and

A: A function is relationship between input and output having condition that for each input there is…

Q: normalization, and strong normalization to explain how many normal forms the term ten has, and if…

A: The lambda-term "ten" is defined as "take 10 [0, 1, 2, ...]" which corresponds to the Haskell…

Q: 10. a. Define clearly but completely: Language L is decidable. b. Let ALLDFA = {M: M is a DFA and…

A: A language L is decidable or recognisable if a Turing machine that recognises (decides) that…

Q: Give an dfa that accepts the language L ((a + b)∗b (a + bb)∗).

A: The DFA for the given language L ((a + b)∗b (a + bb)∗) is shown below:

Q: Let G = (V, E, R, S) be a grammar with V = {S, H, Gm J}; E = {h, g, j}; and the set of rules: %3D…

A: Overview : Automata Theory is a branch of computer science that deals with designing abstract…

Q: Derive the string a*(ab+10) from G:

A: Solution - In the given question, we have to find the Left most and Right most derivation for the…

Q: Let Z={a,b,c}. Show that (b) The set of all languages over Σ is uncountable

A: We need to prove the set of all languages over sigma is uncountable.

Q: Use the pumping lemma to prove that the language L over {a,b,c}", given by L = {wcv: |wa = |vl6} is…

A: First lets see Pumping lemma for regular languages: If a language L is regular, then there exist an…

Q: Construct Parsing Table and DFA for LR(1) Items against following grammer: lexp → atom | list atom →…

A: Actually, given information  lexp → atom | listatom → number | identifierlist → ( lexp-seq )lexp-seq…

Q: ANNSWER BY TRUE OF FULSE: (No need to explain as I already know the answer but I want to check my…

A: All possible patterns of strings can be represented with the help of CFG i.e., context free…

Q: Give a CFG that generates the language { ambkckdª | 2m ≤ n }.

A: Here is the context-free grammar (CFG) which does generates the language { a^mb^kc^kd^n | 2m <= n…

Q: = Use pumping lemma to show that the language L regular {am+1bm} is not

A: Introduction: The Pumping Lemma is used to demonstrate the irregularity of a language. The Pumping…

Q: Let L be L(A), where DFA A = (Q,T,8, q0, F) over alphabet T = {a, %3D b}. Let h be the homomorphism…

A: we formally express the DFA as M  = ( Q, L:, 8, q1, F ) , where Q = {q1, q2 , q3} L: = { a, b}…

Q: Use a closure operation to reduce the language L of all even-lengthed strings of as and bs where…

A:

Q: A stack of blocks can be described by a collection of facts on (Blockl,Block2), which is true if…

A: Answer: A predicate above (Block1, Block2) that is true when block1 is above block2 in the stack is…

Q: Consider the following languages over Σ = {0,1} for L7 is the language described by 1∗(011∗)∗…

A: The breakdown of the regular expression is provided below.

Q: DFA for the language over Σ = {a,b,c} with strings containing an odd number of as, of bs, and of c

A: DFA of the given language

Q: Give the state diagram of a NPDA that recognizes the language L ={anbm | m < n ≤2m}

A: Answer: The NPDA for the given language is as follows:- Now we have to consider m and n; where m = 2…

Q: If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular

A: Explanation : Regular languages are languages that can be recognized by a finite automata. This…

Q: Construct a finite automata that accepts (0,1)

A: The Answer is

Q: Computer Science Show the language L= (w: each occurrence of the substring bb is followed…

A:

Q: Consider the following two variable bindings in Lisp: (setq x ‘(a b c d)) (setq y ‘(4 3 2 1))…

A: General guidance The answer provided below has been developed in a clear step by step manner. First…

Q: Show, formally in terms of DFAs, that if L0 is a regular language (has a DFA) and L1 is a regular…

A: So DFA stands for Deterministic Finite Automata .It can determine the state to which the machine…

Q: The symmetric difference of two sets S, and S2 is defined as S1O S2 = {x:xE S, or xE S2, but x is…

A: Below is the answer to above question. I hope this will be helpful for you...

Q: For each of the following languages LS {a, b}*, show that the elements of the infinite set {a"|n 2…

A: Shown that the given language are pairwise distinguishable

Predicates

A predicate is a function defined with set of variables, which returns the result True or False. The output of a predicate is a Boolean value as a response when given a set of parameters: