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Theory of Computation
Computation includes both arithmetical and non-arithmetic calculations with steps and follows a well-defined model, for example an algorithm. The theory of computation focuses on the three traditional areas i.e.automata, computability, and complexity. Mathematical Notions and Terminologies of Compution are:-
- Sequences and Tuples
- Functions and Relations
- Strings and Languages
- Boolean Logic
The machine will move with the determination of the state of each input symbol in DFA . Because it has a finite number of states, it is called as Deterministic Automaton and hence the machine is called as Deterministic Finite Machine or Deterministic Finite Automaton.
The machine can move to any combination of the states for a particular symbol in NDFA. It is not determined that at which state the machine will move and that is why it is known as non-deterministic Automaton. Beacuase of the finite number of states it is called as Non-deterministic automaton and the machine used is called as Non-deterministic Finite Machine or Nondeterministic Finite Automaton.
Computability Theory consists of The Church–Turing Thesis Decidability Reducibility whereas the Complexity Theory consists of Time complexity Space complexity Tracebility.
- Automata theory
- Computability theory
- Computational complexity theory
Set of operations that used in the computation is termed as model of computation. It is used to measure the complexity of an algorithm. Turing machine is the example of model of computation. Beside this, other models of computation given below:
- Combinatory logic
- Lambda logic
- μ-recursive function
- Register machine
- Markov algorithm
- Programs and computable functions
- Haskell programming language
- Universal program
- Recursive functions
- Turing machines
- Calculation on strings
- Simulation and diagonalization.
- Universality and unsolvable problems
- Kleene's hierarchy and the recursion theorem
- Abstract complexity
- Formal languages
- Propositional logic
- Predicate logic
- Universal language (Lu)
- Diagonalization language (Ld)
- Firmware,Memory addressing
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- Self-modifying machines, cellular automata models (Wolfram), viruses, computer security;Stochastic machines, quantum automata (security revisited), switching networks; Applications of automata theory in coding, secure communication protocols, cryptography.
- Alternative (natural) models of computation: neural networks, evolutionary computing, geneti c algorithms, DNA-computing, swarm technologies are really complex & the complete knowledge of the concepts is required to handle the assignments on these topics.
THEORY OF COMPUTATION:
- Automata and Language Theory, Finite automata, regular expressions, push-down automata, context free grammars, pumping lemmas., Computability Theory, Turing machines, Church-Turing thesis, decidability, halting problem, reducibility
- Complexity Theory, Space Complexity., Randomness in Computation., Circuit Complexity, Interactive Proofs., Approximability and Inapproximability of NP-Hard Problems., Time complexity, Parallel Computation, Approximation and Randomization
- Randomized Computation, Cryptography, Computability, Church Turing thesis, decidable , undecidable problems, elements of recursive function theory, Time complexity, logic, Boolean circuits, NP completeness, Role of randomness in computation, Models of computation,computable,noncomputable functions,space,time complexity,tractable,intractable functions
- Argumention,Logic,rational argument,Common fallacies,Boolean algebra,Axiomatisation,Normal forms,Hardware design ,Programming,Logic gates,Circuits,Simple arithmetic induction,Weak Induction,Strong induction,Structured induction,Propositional logic,Predicate logic,Translation English into logical formulas.
- Propositional semantics,Truth tables,First 0rder Semantics,Satisfiability,Validity,Equivalence,Kleene Algebra,Algorithms,Pseudocode,Efficiency of algorithms,Elementary operations,Examples of maths algorithms,Recurrence ,Recursion,Insertion sort,Optimisation problems,Data structures,Lists,Arrays,Linked lists,Stacks,Queues,Graphs,Trees,Tree traversal,Heaps,Greedy algorithms,Minimum spanning trees,Kruskal's algorithm,Prim's algorithm.
- Dijkstra's algorithm,Greedy heuristics,Divide algorithms,Conquer algorithms,Binary search.,Quicksort algorith,Dynamic programming,Binomial coefficients,Floyd's algorithm,Warsall's algorithm,Greedy heuristics,greedy algorithms.
- Searching and sorting algorithms,Elementary searching ,comparing sequential ,binary and interpolation search ,Binary search trees ,Balanced trees ,B-trees ,Hashing,Graph algorithms:,Depth-first search of undirected and directed graphs ,Articulation points ,Strongly connected components
- Topological sorting of acyclic graphs ,Breadth-first search of directed and undirected graphs ,Network flow ,Ford-Fulkerson method ,Euler circuits,Text algorithms:,String searching ,File compression including Huffman coding ,Cryptology including public key cryptosystems,Analysis of algorithms:,Empirical versus theoretical analysis , Algorithmic complexity ,O notation ,Best worst and average cases ,Classifications of algorithms ,Hierarchies of complexity
- Tractable and intractable problems ,Sums of series ,Simple summation formulae , Estimating a sum using integration,Algorithms with loops:,Nested loops ,Gaussian elimination ,geometric algorithms,Prim's and Kruskal's algorithms,Recursive algorithms and recurrence relations:First-order recurrence relations ,Solving recurrence using the characteristic equation ,Change of variable , conditional asymptotic notation
- maths algorithms including exponentiation and large multiplication,Analysis of searching and sorting algorithms:,Sequential search in ordered and unordered arrays,Binary search,Insertion sort ,mergesort , quicksort,Best case for comparison-based sorting,Reasoning about Programs:,Loop and recursion variants and proving termination,Pre and post-conditions,Loop variants and proving correctness