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دانلود پاورپوینت نظریه زبان ها و ماشین ها (کد9398)

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دانلود پاورپوینت نظریه زبان ها و ماشین ها

\nعنوان پاورپوینت قبلی (عنوان ویرایش نشده) دانلود پاورپوینت نظریه زبان ها و ماشین ها\n

\nعنوان های پاورپوینت : \n\nمراجع درس\n\nسیاست نمره دهی درس\n\nنظریه پیچیدگی\n\nعناوین مورد بحث\n\nنظریه محاسبه پذیری\n\nنظریه ماشین ها\n\nLogic\n\nA Brief History of Logic\n\nA Brief History of Logic\n\nA Brief History of Logic\n\nModern Logic\n\nModern Logic\n\nLogic Types of Interest\n\nSyntax of Propositional Logic\n\nSemantics of Propositional Logic\n\nExamples: (φ  ψ)\n\nExamples: (φ  ψ)\n\nExamples: (φ → ψ)\n\nExamples: (φ ↔ ψ)\n\nExample: (¬φ)\n\nOther Definitions\n\nExamples\n\nFormal System\n\nProof\n\nTheorem\n\nA Formal System for Propositional Logic\n\nExample of a Theorem\n\nExample of a Proof\n\nSoundness and Completeness\n\nPredicate\n\nQuantifiers\n\nQuantifiers: Negation\n\nقواعد استنتاج\n\nDirect Proof\n\nIndirect Proof\n\nProof by Contradiction\n\nProof By Cases\n\nConstructive Existence Proof\n\nاثبات با استقراء\n\nNon-Constructive Existence Proof\n\nIntuitive (Naïve) Set Theory\n\nMembership\n\nExtension\n\nAbstraction\n\nIntuitive versus axiomatic set theory\n\nRussell’s Paradox\n\nGottlob Frege’s Comments\n\nPower Set\n\nSet Operation-Union\n\nSet Operation-Intersection\n\nSet Operation-Complement\n\nOrdered Pairs and n-tuples\n\nOrdered Sets and Set Products\n\nRelations\n\nTypes of Relations on Sets\n\nPartial Order and Equivalence Relations\n\nTotal Ordering\n\nInverse Relation\n\nEquivalence Class\n\nFunctions\n\nFunctions (continued)\n\nFunctions (continued)\n\nCardinality\n\nCardinality (continued)\n\nFinite and Infinite Sets\n\nSome Properties\n\nSome Properties\n\nSome Properties\n\n*1-1 correspondence Q↔N\n\nCountable Sets\n\nDiagonal Argument\n\nUncountable Sets\n\nTransfinite Cardinal Numbers\n\nالفبا\n\nرشته ها\n\nاعمال روی رشته ها\n\nاعمال روی الفبا\n\nزبان ها\n\nاعمال روی زبان ها\n\nاعمال روی زبان ها\n\nاعمال روی زبان ها\n\nاعمال روی زبان ها\n\nGödel Numbering\n\n \n\n

\n\nقسمت ها و تکه های اتفاقی از فایل\n\nنظریه زبان ها و ماشین ها\n\n2pro.ir\n\nمراجع درس\n\nمرجع اصلی:\n\nM. Sipser, ”Introduction to the Theory of Computation,” 2nd Ed., Thompson Learning Inc., 2006.\n\nمراجع کمکی:\n\nP. Linz, “An Introduction to Formal Languages and Automata,” 3rd Ed., Jones and Barlett Publishers, Inc., 2001.\n\nJ.E. Hopcroft, R. Motwani and J.D. Ullman, “Introduction to Automata Theory, Languages, and Computation,” 2nd Ed., Addison-Wesley, 2001.\n\nP.J. Denning, J.B. Dennnis, and J.E. Qualitz, “Machines, Languages, and Computation,” Prentice-Hall, Inc., 1978.\n\nP.J. Cameron, “Sets, Logic and Categories,” Springer-Verlag, London limited, 1998.\n\nسیاست نمره دهی درس\n\n \n\nتمرینات %15\n\nارائه تحقیقاتی %10\n\nکوییز 1 عمومی درس %20\n\nکوییز 2عمومی درس %25\n\nآزمون پایان نیمسال %30\n\nنظریه پیچیدگی\n\nدانش رده بندی مسائل بر اساس سختی محاسباتی\n\nبرای غلبه بر پیچیدگی چه می توان کرد؟\n\nتغییر مسئله پس از کشف که عامل دشواری آن\n\nتقریب زدن راه حل مسئله\n\nارائه روش هایی که در حالت متوسط عملکرد خوبی دارند؛\n\nاستفاده از روش های تصادفی\n\nکاربردها\n\nبه عنوان مثال در رمزنگاری، هدف این است که رمزگشایی با توان محاسباتی مهاجم غیرممکن باشد.\n\nعناوین مورد بحث\n\nنظریه پیچیدگی\n\nنظریه محاسبه پذیری\n\nنظریه ماشین ها\n\nمبانی ریاضی\n\nالفبا\n\nرشته ها\n\nزبان ها\n\n \n\n \n\n \n\nنظریه محاسبه پذیری\n\nماشین ها چه مسائلی را می توانند حل کنند؟\n\nرده بندی مسائل در دو گروه قابل محاسبه و غیرقابل محاسبه\n\n \n\nمدل های نظری برای ماشین ها\n\nبه علت قدرتمندی مدل هایی مانند RAM یا ماشین تورینگ اثبات این که چه مسائلی را می توانند حل کنند دشوار است.\n\nنظریه ماشین ها\n\nتعریف و ویژگی های مدل های ریاضی محاسبه\n\nمدل ماشین حالت متناهی\n\nدر پردازش متن، کامپایلرها و طراحی سخت افزار کاربرد دارد.\n\nمدل ماشین پشته ای\n\nدر زبان های برنامه سازی و هوش مصنوعی کاربرد دارد.\n\n \n\nLogic\n\nA Brief History of Logic\n\nDefinition: Logic is the science of the formal principles of reasoning.\n\nLogic was known as 'dialectic' or 'analytic' in Ancient Greece. The word 'logic' (from the Greek logos, meaning discourse or sentence) does not appear in the modern sense until the commentaries of Alexander of Aphrodisias, writing in the third century A.D.\n\n \n\nA Brief History of Logic\n\nWhile many cultures have employed intricate systems of reasoning, and logical methods are evident in all human thought, an explicit analysis of the principles of reasoning was developed only in three traditions: those of China, India, and Greece.\n\nAlthough exact dates are uncertain, particularly in the case of India, it is possible that logic emerged in all three societies by the 4th century BC.\n\nA Brief History of Logic\n\nThe formally sophisticated treatment of modern logic descends from the Greek tradition, particularly Aristotelian logic, which was further developed by Islamic Logicians and then medieval European logicians.\n\nThe work of Frege in the 19th century marked a radical departure from the Aristotlian leading to the rapid development of symbolic logic, later called mathematical logic.\n\n \n\nModern Logic\n\nDescartes proposed using algebra, especially techniques for solving for unknown quantities in equations, as a vehicle for scientific exploration.\n\nThe idea of a calculus of reasoning was also developed by Leibniz. He was the first to formulate the notion of a broadly applicable system of mathematical logic.\n\nFrege in his 1879 work extended formal logic beyond propositional logic to include quantification to represent the "all", "some" propositions of Aristotelian logic.\n\nModern Logic\n\nA logic is a language of formulas.\n\nA formula is a finite sequence of symbols with a syntax and semantics.\n\nA logic can have a formal system.\n\nA formal system consists of a set of axioms and rules of inference.\n\n \n\n \n\nLogic Types of Interest\n\nPropositional Logic\n\nPredicate Logic\n\n \n\nSyntax of Propositional Logic\n\nLet {p0, p1, ..} be a countable set of propositional variables,\n\n{, , ¬, →, ↔} be a finite set of connectives,\n\nAlso, there are left and right brackets,\n\nA propositional variable is a formula,\n\nIf φ and ψ are formulas, then so are (¬φ), (φ  ψ), (φ  ψ), (φ → ψ), and (φ ↔ ψ).\n\n \n\n \n\nSemantics of Propositional Logic\n\nAny formula, which involves the propositional variables p0,...,pn , can be used to define a function of n variables, that is, a function from the set {T, F}n to {T, F}. This function is often represented as the truth table of the formula and is defined to be the semantics of that formula.\n\nExamples: (φ  ψ)\n\nExamples: (φ  ψ)\n\nExamples: (φ → ψ)\n\nExamples: (φ ↔ ψ)\n\nExample: (¬φ)\n\nOther Definitions\n\nA formulae is a tautology if it is always true.\n\nA formulae is a contradiction if it is never true.\n\nA formulae is a contingency if it is sometimes true.\n\n \n\n \n\n \n\nExamples\n\n(P  (¬P)) is a tautology.\n\n(P  (¬P)) is a contradiction.\n\n(P → (¬P)) is a contingency.\n\n \n\nFormal System\n\nA formal system includes the following:\n\nAn alphabet A, a set of symbols.\n\nA set of formulae, each of which is a string of symbols from A.\n\nA set of axioms, each axiom being a formula.\n\nA set of rules of inference, each of which takes as ‘input’ a finite sequence of formulae and produces as output a formula.\n\n \n\nProof\n\nA proof in a formal system is just a finite sequence of formulae such that each formula in the sequence either is an axiom or is obtained from earlier formulae by applying a rule of inference.\n\nTheorem\n\nA theorem of the formal system is just the last formula in a proof.\n\nA Formal System for Propositional Logic\n\nThere are three ‘schemes’ of axioms, namely:\n\n(A1) (φ→(ψ → φ))\n\n(A2) (φ→(ψ → θ)) → ((φ→ ψ) → (φ → θ))\n\n(A3) (((¬φ) →(¬ψ)) → (ψ → φ))\n\nEach of these formulas is an axiom, for all choices of formulae φ, ψ, θ.\n\nThere is only one rule of inference, namely Modus Ponens: From φ and (φ→ ψ), infer ψ.\n\nExample of a Theorem\n\nFor any formula φ, the formula (φ→φ) is a theorem of the propositional logic.\n\nExample of a Proof\n\nUsing (A2), taking φ, ψ, θ to be φ, (φ→φ) and φ respectively\n\n((φ→((φ→φ)→φ))→((φ→(φ→φ))→(φ →φ)))\n\nUsing (A1), taking φ, ψ to be φ and (φ→φ) respectively\n\n(φ→((φ→φ)→φ))\n\nUsing Modus Ponens\n\n((φ→(φ→φ))→(φ →φ))\n\nUsing (A1), taking φ, ψ to be φ and φ respectively\n\n(φ→(φ→φ))\n\nUsing Modus Ponens\n\n(φ→φ)\n\n \n\n \n\n \n\nSoundness and Completeness\n\nA formal system is said to be sound if all theorems in that system are tautology.\n\nA formal system is said to be complete if all tautologies in that system are theorems.\n\nPredicate\n\nA proposition involving some variables, functions and relations\n\n \n\nExample:\n\nQuantifiers\n\n \n\n \n\n \n\n \n\nQuantifiers: Negation\n\n \n\n \n\n \n\n \n\nقواعد استنتاج\n\nModus ponens\n\nبرهان خلف\n\nConjunction\n\nاثبات با مورد\n\nاستقراء\n\n \n\nDirect Proof\n\nIf the two propositions (premises) p and p → q are theorems, we may deduce that the proposition q is also a theorem.\n\nThis fundamental rule of inference is called modus ponens by logicians.\n\nIndirect Proof\n\nProves p → q by instead proving the contra-positive, ~q → ~p\n\nProof by Contradiction\n\nThe rule of inference used is that from theorems p and ¬q → ¬p, we may deduce theorem q.\n\nProof By Cases\n\nYou want to prove p → q\n\nP can be decomposed to some cases:\n\np ↔ p1 ν p2 ν …ν pn\n\n \n\nindependently prove the n implications given by\n\npi → q for 1 ≤ i ≤ n.\n\nConstructive Existence Proof\n\nWant to prove that .\n\n \n\nFind an a and then prove that P(a) is true\n\nاثبات با استقراء\n\nTo prove\n\n \n\n \n\n1) Proof P(0),\n\n2) Proof\n\n \n\n \n\nNon-Constructive Existence Proof\n\nWant to prove that .\n\nYou cannot find an a that P(a) is true\n\n \n\nThen, you can use proof by contradiction:\n\n \n\n \n\n \n\nIntuitive (Naïve) Set Theory\n\nThere are three basic concepts in set\n\ntheory:\n\n \n\nMembership\n\nExtension\n\nAbstraction\n\n \n\nMembership\n\nMembership is a relation that holds between a set and an object\n\n \n\nto mean “the object x is a member of the set A”, or “x belongs to\n\nA”. The negation of this assertion is written\n\n \n\nas an abbreviation for the proposition\n\n \n\nOne way to specify a set is to list its elements. For example, the set\n\nA = {a, b, c}\n\nconsists of three elements. For this set A, it is true that\n\nbut\n\nExtension\n\nThe concept of extension is that two sets are identical\n\nif and if only if they contain the same elements. Thus\n\nwe write A=B to mean\n\n \n\nAbstraction\n\nEach property defines a set, and each set defines a\n\nproperty\n\n \n\nIf p(x) is a property then we can define a set A\n\n \n\n \n\nIf A is a set then we can define a predicate p(x)\n\n \n\n \n\nIntuitive versus axiomatic set theory\n\n \n\nThe theory of set built on the intuitive concept of membership, extension, and abstraction is known as intuitive (naïve) set theory.\n\nAs an axiomatic theory of sets, it is not entirely satisfactory, because the principle of abstraction leads to contradictions when applied to certain simple predicates.\n\nRussell’s Paradox\n\nLet p(X) be a predicate defined as\n\n \n\nP(X) = (XX)\n\nDefine set R as\n\n \n\nR={X|P(X)}\n\nIs P(R) true?\n\nIs P(R) false?\n\n \n\n \n\nGottlob Frege’s Comments\n\nThe logician Gottlob Frege was the first to develop mathematics on the foundation of set theory. He learned of Russell Paradox while his work was in press, and wrote, “A scientist can hardly meet with anything more undesirable than to have the foundation give way just as the work is finished. In this position I was put by a letter from Mr. Bertrand Russell as the work was nearly through the press.”\n\nPower Set\n\nThe set of all subsets of a given set A is\n\nknown as the power set of A, and is\n\ndenoted by P(A):\n\n \n\nP(A) = {B | B  A}\n\nSet Operation-Union\n\nThe union of two sets A and B is\n\nA  B = {x | (x  A)  (x  B)}\n\nand consists of those elements in at least one of A and B.\n\n \n\nIf A1, …, An constitute a family of sets, their union is\n\n= (A1  …  An)\n\n \n\n= {x| x  Ai for some i, 1≤ i ≤ n}\n\nSet Operation-Intersection\n\nThe intersection of two sets A and B is\n\nA  B = {x | (x  A) (x  B)}\n\nand consists of those elements in at least one of A and B.\n\n \n\nIf A1, …, An constitute a family of sets, their intersection is\n\n \n\n= (A1  …  An)\n\n \n\n= {x| x  Ai for all i, 1≤ i ≤ n}\n\nSet Operation-Complement\n\nThe complement of a set A is a set Ac defined as:\n\nAc = {x | x A}\n\n \n\nThe complement of a set B with respect to A, also denoted as A-B, is defined as:\n\nAc = {x A | x B}\n\n \n\nOrdered Pairs and n-tuples\n\nAn ordered pair of elements is written\n\n(x,y)\n\nwhere x is known as the first element, and y is known\n\nas the second element.\n\n \n\nAn n-tuple is an ordered sequence of elements\n\n(x1, x2, …, xn)\n\nAnd is a generalization of an ordered pair.\n\nOrdered Sets and Set Products\n\nBy Cartesian product of two sets A and B, we mean the set\n\n \n\nA×B = {(x,y)|xA , yB}\n\n \n\nSimilarly,\n\n \n\nA1×A2×…An = {x1A1, x2A2, …, xnAn}\n\n \n\n \n\nRelations\n\nA relation ρ between sets A and B is a subset of A×B:\n\nρ  A×B\n\n \n\nThe domain of ρ is defined as\n\nDρ = {x  A | for some y  B, (x,y)  ρ}\n\n \n\nThe range of ρ is defined as\n\nRρ = {y  B | for some x  A, (x,y)  ρ}\n\n \n\nIf ρ  A×A, then ρ is called a ”relation on A”.\n\n \n\n \n\n \n\n \n\n \n\n \n\nTypes of Relations on Sets\n\nA relation ρ is reflexive if\n\n(x,x) ρ, for each xA\n\nA relation ρ is symmetric if, for all x,yA\n\n(x,y) ρ implies (y,x) ρ\n\nA relation ρ is antisymmetric if, for all x,yA\n\n(x,y) ρ and (y,x) ρ implies x=y\n\nA relation ρ is transitive if, for all x,y,zA\n\n(x,y) ρ and (y,z) ρ implies (x,z) ρ\n\n \n\n \n\n \n\n \n\nPartial Order and Equivalence Relations\n\nA relation ρ on a set A is called a partial ordering of A if ρ is reflexive, anti-symmetric, and transitive.\n\nA relation ρ on a set A is called an equivalence relation if ρ is reflexive, symmetric, and transitive.\n\n \n\nTotal Ordering\n\nA relation ρ on a set A is a total ordering if ρ is a partial ordering and, for each pair of elements (x,y) in A×A at least one of (x,y)ρ or (y,x)ρ is true.\n\nInverse Relation\n\nFor any relation ρ  A×B, the inverse of ρ is defined by\n\nρ-1 = {(y,x) | (x,Y)  ρ}\n\n \n\nIf Dρ and Rρ are the domain and range of ρ, then\n\nDρ-1 = Dρ and Rρ-1 = Rρ\n\n \n\n \n\n \n\n \n\nEquivalence Class\n\nLet ρ  A×A be an equivalence relation on A. The equivalence class of an element x is defined as\n\n[x] = {y  A | (x,y)  ρ}\n\n \n\nAn equivalence relation on a set partitions the set.\n\nFunctions\n\nA relation f  A× B is a function if it has the property\n\n(x,y) f and (x,z) f implies y=z\n\nIf f  A× B is a function, we write\n\nf: A → B\n\nand say that f maps A into B. We use the common notation\n\nY = f(x)\n\nto mean (x,y)  f.\n\nAs before, the domain of f is the set\n\nDf = {x A | for some y B, (x,y)  f}\n\nand the range of f is the set\n\nRf = {y B | for some x  A, (x,y)  f}\n\nIf Df  A, we say the function is a partial function; if Df = A, we say that f is a total function.\n\n \n\n \n\n \n\nFunctions (continued)\n\nIf x  Df, we say that f is defined at x; otherwise f is undefined at x.\n\nIf Rf = B, we say that f maps Df onto B.\n\nIf a function f has the property\n\nf(x) = z and f(y) = z implies x = y\n\nthen f is a one-to-one function. If f: A → B is a\n\none-to-one function, f gives a one-to-one\n\ncorrespondence between elements of its domain\n\nand range.\n\nFunctions (continued)\n\nLet X be a set and suppose A  X. Define function\n\nCA: X → {0,1}\n\nsuch that CA(x) = 1, if x A; CA(x) = 0, otherwise. CA(x) is called the characteristic function of set A with respect to set X.\n\nIf f  A× B is a function, then the inverse of f is the set\n\nf-1 = {(y,x) | (x,y)  f}\n\nf-1 is a function if and only if f is one-to-one.\n\nLet f: A → B be a function, and suppose that X  A. Then the set\n\nY = f(X) = {y  B | y = f(x) for some x  X}\n\nis known as the image of X under f.\n\nSimilarly, the inverse image of a set Y included in the range of f is\n\nf-1(Y) = {x  A | y = f(x) for some y  Y}\n\n \n\n \n\n \n\n \n\nCardinality\n\nTwo sets A and B are of equal cardinality, written as\n\n|A| = |B|\n\nif and only if there is a one-to-one function f: A → B\n\nthat maps A onto B.\n\nWe write\n\n|A| ≤ |B|\n\nif B includes a subset C such that |A| = |C|.\n\nIf |A| ≤ |B| and |A| ≠ |B|, then A has cardinality less than that of B, and we write\n\n|A| < |B|\n\n \n\n \n\n \n\n \n\n \n\n \n\nCardinality (continued)\n\nLet J = {1, 2, …} and Jn = {1, 2, …, n}.\n\nA sequence on a set X is a function f: J → X. A sequence may be written as\n\nf(1), f(2), f(3), …\n\nHowever, we often use the simpler notation\n\nx1, x2, x3, …., xi  X\n\nA finite sequence of length n on X is a function\n\nf: Jn → X, usually written as\n\nx1, x2, x3, …., xn, xi  X\n\nThe sequence of length zero is the function f: → X.\n\n \n\nFinite and Infinite Sets\n\nA set A is finite if |A| = |jn| for some integer n≥0, in which case we say that A has cardinality n.\n\nA set is infinite if it is not finite.\n\nA set X is denumerable if |X| = |j|. A set is countable if it is either finite or denumerable.\n\nA set is uncountable if it is not countable.\n\nSome Properties\n\nProposition: Every subset of J is countable. Consequently, each subset of any denumerable set is countable.\n\nProposition: A function f: J → Y has a countable range. Hence any function on a countable domain has a countable range.\n\nProposition: The set J × J is denumerable. Therefore, A × B is countable for arbitrary countable sets A and B.\n\n \n\nSome Properties\n\nProposition: The set A  B is countable whenever A and B are countable sets.\n\n \n\nProposition: Every infinite set X is at least denumerable ; that is |X| ≥ |J|.\n\n \n\nProposition: The set of all infinite sequence on {0, 1} is uncountable.\n\n \n\nSome Properties\n\nProposition: (Schröder-Bernestein Theorem)\n\nFor any set A and B, if |A| ≥ |B| and |B| ≥ |A|,\n\nthen |A| = |B|.\n\n \n\nProposition: (Cantor’s Theorem)\n\nFor any set X,\n\n|X| < |P(X)|.\n\n \n\n*1-1 correspondence Q↔N\n\nProof (dove-tailing):\n\nCountable Sets\n\nAny subset of a countable set\n\nThe set of integers, algebraic/rational numbers\n\nThe union of two/finite number of countable sets\n\nCartesian product of a finite number of countable sets\n\nThe set of all finite subsets of N;\n\nSet of binary strings\n\n \n\nDiagonal Argument\n\nUncountable Sets\n\nR, R2, P(N)\n\nThe intervals [0,1), [0, 1], (0, 1)\n\nThe set of all real numbers;\n\nThe set of all functions from N to {0, 1};\n\nThe set of functions N → N;\n\nAny set having an uncountable subset\n\n \n\nTransfinite Cardinal Numbers\n\nCardinality of a finite set is simply the number of elements in the set.\n\nCardinalities of infinite sets are not natural numbers, but are special objects called transfinite cardinal numbers\n\n \n\n0:|N|, is the first transfinite cardinal number.\n\n \n\ncontinuum hypothesis claims that |R|=1, the second transfinite cardinal.\n\n \n\nالفبا\n\nالفبا\n\nمجموعه ای متناهی , و غیرتهی از علائم الفبایی (معمولاً با ∑ یا Г نمایش داده می شود)\n\nمثال:\n\nرشته ها\n\nرشته\n\nدنباله ای متناهی از علائم یک الفبا\n\nمثال:\n\nطول رشته ω که با |ω| نشان داده می شود تعداد علائم موجود در رشته است.\n\nرشته تهی(ε یا λ) رشته ای با طول صفر است.\n\n \n\n \n\nیک زیررشته(substring) زیردنباله ای شامل علائم متوالی از رشته است.\n\n \n\nاعمال روی رشته ها\n\nمقلوب یک رشته\n\nمثال:\n\n \n\nالحاق رشته ها\n\nمثال:\n\n \n\n \n\nاعمال روی الفبا\n\nعملگر *:\n\nمجموعه تمام رشته هایی که از الفبای ∑ قابل تولید هستند.\n\n \n\n \n\n \n\nعملگر +:\n\nمجموعه تمام رشته ها به جز λ که از الفبای ∑ قابل تولید هستند. فرض کنید = {λ} . آنگاه\n\n \n\n \n\nزبان ها\n\nزبان\n\nمجموعه ای از رشته ها روی یک الفبای معین\n\nهر زبان روی یک الفبای ∑، زیر مجموعه ای از *∑ است.\n\nمثال:\n\nاعمال روی زبان ها\n\nزبان ها نوعی خاص از مجموعه هستند و اعمال روی مجموعه ها در آن ها نیز قابل تعریف است.\n\n \n\nاجتماع\n\nاشتراک\n\nتفاضل\n\n \n\nمتمم\n\nاعمال روی زبان ها\n\nمقلوب یک زبان:\n\n \n\nمثال:\n\nاعمال روی زبان ها\n\nالحاق(Concatenation) دو زبان:\n\n \n\n \n\n \n\n \n\nمثال:\n\nاعمال روی زبان ها\n\nعملگر * (Kleene *):\n\nمجموعه تمام رشته هایی که با الحاق رشته های یک زبان قابل تولید هستند.\n\n \n\nمثال:\n\n \n\n \n\n \n\n \n\n \n\n \n\nعملگر + نیز مانند عملگر * است با این تفاوت که رشته λ در مجموعه حاصل نیست.\n\n \n\n \n\nGödel Numbering\n\nLet be an alphabet containing n objects. Let h: → Jn be an arbitrary one-to-one correspondence. Define function f as:\n\nf: → N\n\nsuch that f(ε) =0; f(w.v) = n f(w) + h(v), for w and v .\n\nf is called a Gödel Numbering of .\n\n \n\nProposition: is denumerable.\n\n \n\nProposition: Any language on an alphabet is countable.\n\n \n\n \n\n \n\nبا تشکر از توجه شما\n\nتو پروژه\n\n2pro.ir\n\n \n\n \n\n۳۰ تا ۷۰ درصد پروژه / پاورپوینت / پاور پوینت / سمینار / طرح های کار افرینی / طرح توجیهی / پایان نامه/ مقاله ( کتاب ) های اماده به صورت رایگان میباشد