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Computational complexity theory can be defined as a branch of theory of computation in mathematics & theoretical computer science. It focuses on organizing computational problems  on the basis of their inherent difficulty. A computational problem refers to be a task which is in principle willing for being solved through a computer system. Complexity theory can be defined as the body of knowledge which is concerned with the fundamental principles of computation. Its starting may be traced to the use of asymptotic complexity as well as reducibility.
The modern complexity theory is the outcome of activities of research in electrical engineers who develop switching theory as a tool for the purpose of hardware design, various biologists who are studying models for neuron nets or evolution, mathematicians who work on the foundations of logic as well as arithmetics, linguists who investigate grammars for natural languages, physicists who study the implications of building Quantum computers & computer scientists who search searching for effective & efficient algorithms for difficult problems.
All these are the areas in which computational complexity theory is used. Basically, a computational problem includes of instances of problem as well as solutions to these instances of problem. If large amounts of resources such as time, communications, storage, processors, circuit gates, etc are needed for solving a problem then the problem is considered to be difficult regardless of algorithm that has been used. There is a subset of computational complexity theory called analysis of algorithms by which theoretical estimates are provided for the resources required for particular algorithms. 
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Topics for Computational Complexity Theory Assignment help :

  • Cooks theorem,Probabilistic Algorithms, Complexity analysis of probabilistic algorithms, complexity classes PP , BPP, Space complexity, Savitchs theorem, Exponential time, Non elementary problems, quantitative theory of computation,Time complexity of algorithmic problems, structure of P NP PH PSPACE, randomized algorithms, advice machines, Boolean circuits, Kolmogorov complexity,Deterministic time.
  • Non deterministic time,space complexity, complexity classes, complete problems, Time hierarchies, space hierarchies, polynomial time hierarchy, Circuit complexity, Probabilistic computation, Exponential complexity lower , Bounds, Interactive proofs, Lower bounds for Boolean circuits, Design of space efficient algorithm, Undirected graph reachability problem, Hardness based derandomization of randomized algorithms, Probabilistic proof characterization of non-deterministic,Computation modes, Deterministic Turing machines, Equivalent Turing machines.

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  • Context free grammars Equivalence with push-down automata, model of computation, Grammars/Regular Expressions, Computable languages, Invariance under varying number of tapes/alphabet/random access machines,  Decidability,languages unsolvable with TMs, Undecidability,diagonalisation as a , roof method, Resource-bounded computation,big O notation, Time and space bounds on TMs, complexity classes,Hierarchy theorems,Inclusion of time and space classes,Nondeterminism and the NP complexity class,NP-hard and NP-complete problems, ATisfiability problem,reductions between NP-complete problems,Graph Isomorphism/Hamilton Cycle/Clique,Best case/average case/worst case,Approximate algorithms,inear , programming and integer linear programming,Complexity analysis of algorithms
  • Common sorting/search problems,maximum matching,simple graph algorithms, ,Complexity Theory , P vs. NP, Deterministic Hierarchy Theorems, Space Complexity,Nl=coNL, Polynomial Hierarchy,Boolean Circuits , Randomized Computation ,Valiant-Vairani Slides , Counting Problems , Interactive Proofs , IP=PSPACE Warmup,Undirected Connectivity, Eigenvalues ,Eigenvalues and Random Walks, UCONN in RL , Quasi-Random Properties ,PRGs ,PRGs , Zig-Zag Product and Expanders,L=SL and Quantum,computing,Quantum Computing, No-cloning theorem and Quantum Teleportation, Deutsch-Jozsa Algorithm
  • Models of Computation,Deterministic Turing machines,Equivalent Turing machines,Register machines,Language recognition,Language acceptance,Recursive languages,Recursively enumerable languages, Halting Problem,Problem reduction,Undecidability of the tiling problem,Undecidability of first-order logic,Other unsolvable problems,Non-deterministic Turing machines,Polynomial-time reduction, Elementary properties of polynomial time reduction,complexity classes P, NP, NP-complete,Cook's theorem,Space complexity,Savitch’s theorem,Exponential time,Non-elementary problems
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