Logic I Fall 2009 Problem Set 5
... Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete iff a language with ...
... Problem Set 5 In class I talked about SL being truth-functionally complete (TF-complete). For the problems below, use TLB’s definition of TF-completeness, according to which it is sets of connectives that are (or aren’t) TF-complete: Definition: A set of connectives is TF-complete iff a language with ...
review1
... 2. When using the method System.out.printf( ), what is the purpose of the %d format code? 3. What does it mean for the return type of a method to be void? 4. What Java keyword is used when invoking a constructor? 5. Suppose a is a one-dimensional array of double. Fill in the blanks in the following ...
... 2. When using the method System.out.printf( ), what is the purpose of the %d format code? 3. What does it mean for the return type of a method to be void? 4. What Java keyword is used when invoking a constructor? 5. Suppose a is a one-dimensional array of double. Fill in the blanks in the following ...
The Open World of Super-Recursive Algorithms and
... people are working with displays and computers produce their results mostly on the screen of a monitor. These results on the screen exist there only if the computer functions. If this computer halts, then the result on its screen disappears. This is opposite to the basic condition on ordinary (recur ...
... people are working with displays and computers produce their results mostly on the screen of a monitor. These results on the screen exist there only if the computer functions. If this computer halts, then the result on its screen disappears. This is opposite to the basic condition on ordinary (recur ...
CS-2852 Data Structures
... • Some functional programming languages don’t have loops (equivalent to imperative looping constructs) • A function “calls itself” – directly or not CS-2852 Data Structures, Andrew J. Wozniewicz ...
... • Some functional programming languages don’t have loops (equivalent to imperative looping constructs) • A function “calls itself” – directly or not CS-2852 Data Structures, Andrew J. Wozniewicz ...
Hierarchical Introspective Logics
... existence of assertions concerning the natural integers that are not provable modulo the proof rules of specific given formal systems and also of the general results on undecidability which also imply the existence of such assertions that are true but not provable in the context of a given formal sy ...
... existence of assertions concerning the natural integers that are not provable modulo the proof rules of specific given formal systems and also of the general results on undecidability which also imply the existence of such assertions that are true but not provable in the context of a given formal sy ...
Chomsky Hierarchy Language Operations and Properties
... languages (it can either accept or reject a string). They are also called Recursive. • Partially Computable Languages most of the times are called Recognizable because a Turing Machine can recognize a string in the language (accept it) but it might not be able to decide if a string is not in the lan ...
... languages (it can either accept or reject a string). They are also called Recursive. • Partially Computable Languages most of the times are called Recognizable because a Turing Machine can recognize a string in the language (accept it) but it might not be able to decide if a string is not in the lan ...
Recursion Review - Department of Computer Science
... The total number of function calls is proportional to the total number of nodes of the recursion tree ...
... The total number of function calls is proportional to the total number of nodes of the recursion tree ...
Gödel`s Incompleteness Theorem
... branch of mathematics, there would always be some propositions that couldn't be proven either true or false using the rules and axioms ... of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to ...
... branch of mathematics, there would always be some propositions that couldn't be proven either true or false using the rules and axioms ... of that mathematical branch itself. You might be able to prove every conceivable statement about numbers within a system by going outside the system in order to ...
ppt
... “All Cretans are liars.” Equivalently: “This statement is false.” Russell’s types can help with the set paradox, but not with this one. ...
... “All Cretans are liars.” Equivalently: “This statement is false.” Russell’s types can help with the set paradox, but not with this one. ...
Slides
... It is with this analysis, and its impact on the minds of such men as John von Neumann and others, that the theoretical concepts and the analysis of the digital computer in the modern sense began. It remains true to this very day that the theoretical description of what can be computed in general an ...
... It is with this analysis, and its impact on the minds of such men as John von Neumann and others, that the theoretical concepts and the analysis of the digital computer in the modern sense began. It remains true to this very day that the theoretical description of what can be computed in general an ...
lecture05
... [what 2nd order quantifiers did we need ?] – The graph is 3-colorable – The graph has a Hamiltonean path ...
... [what 2nd order quantifiers did we need ?] – The graph is 3-colorable – The graph has a Hamiltonean path ...
hilbert systems - CSA
... S U {~X} is also Consistent If not, S U {~X} |- X S |- (~X > X) { Deduction Theorem } (~X > X) > X { Theorem } S |- X { Modus Ponens } S U {~X} is satisfiable { Model Existence Theorem } S U {X} is not valid. ...
... S U {~X} is also Consistent If not, S U {~X} |- X S |- (~X > X) { Deduction Theorem } (~X > X) > X { Theorem } S |- X { Modus Ponens } S U {~X} is satisfiable { Model Existence Theorem } S U {X} is not valid. ...
Python Programming: An Introduction to Computer - comp
... • n: the number of disks • moving the disks from A to B via C • no larger disks put on top of smaller disks • A recursive approach: • Base: trivial and solved for n = 1 • Induction; for n > 1, solveTowers(n, A, B, C) can be solved by • solveTowers(n - 1, A, C, B) // the top n-1 disks • solveTowers(1 ...
... • n: the number of disks • moving the disks from A to B via C • no larger disks put on top of smaller disks • A recursive approach: • Base: trivial and solved for n = 1 • Induction; for n > 1, solveTowers(n, A, B, C) can be solved by • solveTowers(n - 1, A, C, B) // the top n-1 disks • solveTowers(1 ...
Recursion
... The process of solving a problem by reducing it to smaller versions of itself is called recursion. Example: Consider the concept of factorials ...
... The process of solving a problem by reducing it to smaller versions of itself is called recursion. Example: Consider the concept of factorials ...
Lambda λ Calculus
... overhead in time” - Weak Invariance Thesis, Slot and van Emde Boas’ Much like we have proven with the 3-CNF Reductions in class we must prove any lambda calculus function can be reduced to another. ß-Reduction: (λx. M)N → ßM[N/x] ...
... overhead in time” - Weak Invariance Thesis, Slot and van Emde Boas’ Much like we have proven with the 3-CNF Reductions in class we must prove any lambda calculus function can be reduced to another. ß-Reduction: (λx. M)N → ßM[N/x] ...
Different notions of conuity and intensional models for λ
... Let < A, ≤> be any complete and co-complete poset (partially ordered set), P a generalized sequence of its elements (i.e. a sequence with directed set of indexes, not necessarily equal to the set of naturals). Then, in the case if P is increasing (decreasing), we define its limit as the least upper ...
... Let < A, ≤> be any complete and co-complete poset (partially ordered set), P a generalized sequence of its elements (i.e. a sequence with directed set of indexes, not necessarily equal to the set of naturals). Then, in the case if P is increasing (decreasing), we define its limit as the least upper ...
Deployment of Sensing Devices on Critical Infrastructure
... Once the base case has been reached, the solution begins. ...
... Once the base case has been reached, the solution begins. ...
310409-Theory of computation
... • The union of sets A and B, written A B, is a set that contains everything that is in A, or in B, or in both. • The intersection of sets A and B, written A B, is a set that contains exactly those elements that are in both A and B. • The set difference of set A and set B, written A - B, is a set ...
... • The union of sets A and B, written A B, is a set that contains everything that is in A, or in B, or in both. • The intersection of sets A and B, written A B, is a set that contains exactly those elements that are in both A and B. • The set difference of set A and set B, written A - B, is a set ...
pdf
... We do however know that the 3x+1 function, call it f in this slide, is a partial function from numbers to numbers, thus for any n, f(n) is a number if it converges (halts) number if it converges (halts). ...
... We do however know that the 3x+1 function, call it f in this slide, is a partial function from numbers to numbers, thus for any n, f(n) is a number if it converges (halts) number if it converges (halts). ...
Playing Chess with a Philosopher: Turing and Wittgenstein
... Provide clarity to the concepts we use in mathematics. • Clarify notions such as “identity”, “proof”, “rule following”, “axioms”, “contradiction”, “errors” and “mistakes” in calculation. ...
... Provide clarity to the concepts we use in mathematics. • Clarify notions such as “identity”, “proof”, “rule following”, “axioms”, “contradiction”, “errors” and “mistakes” in calculation. ...
Lecture
... • Is the algorithm or data structure naturally suited to recursion? A list, such as data read from the keyboard, is not naturally recursive structure. Moreover, the algorithm is not a logarithmic algorithm. • Is the recursive solution shorter and more understandable? Yes • Does the recursive solutio ...
... • Is the algorithm or data structure naturally suited to recursion? A list, such as data read from the keyboard, is not naturally recursive structure. Moreover, the algorithm is not a logarithmic algorithm. • Is the recursive solution shorter and more understandable? Yes • Does the recursive solutio ...
Theory - NUS School of Computing
... and moves the head right, and goes to Step 2. Step 2: If the symbol being read is 1, then write a 0, move the head right, and Repeat Step 2. If the symbol being read is B, then move right, and go to Step 3. Step 3: If the symbol begin read is 1, then write a 2, move the head right, and repeat Step 3 ...
... and moves the head right, and goes to Step 2. Step 2: If the symbol being read is 1, then write a 0, move the head right, and Repeat Step 2. If the symbol being read is B, then move right, and go to Step 3. Step 3: If the symbol begin read is 1, then write a 2, move the head right, and repeat Step 3 ...