# Foundations of Computer Science

@article{Nambiar1997FoundationsOC, title={Foundations of Computer Science}, author={K. Kannan Nambiar}, journal={Mathematics eJournal}, year={1997} }

A machine equivalent to Turing machine, that is more intuitive in its working is defined. Three derivation rules are added to Elementary Arithmetic of Godel and his incompleteness theorems are proved without using any metalanguage. Two axioms are added to Zermelo-Fraenkel theory to derive the Continuum Hypothesis and to split the unit interval into infinitesimals.

## 343 Citations

Pseudorandom generators hard for propositional proof systems

- Computer Science, Mathematics
- 2009

Based on the concept of pseudorandom generators, the notation of a generator which is hard for a proof system is introduced. Such a generator admits a superpolynomial lower bound. For the resolution…

Abstractions, their algorithms, and their compilers

- Computer ScienceCommun. ACM
- 2022

Jeffrey D. Ullman and Alfred V. Aho are recipients of the 2020 ACM A.M. Turing award. They were recognized for creating fundamental algorithms and theory underlying programming language…

Quantum Algorithms Are Determining the Property of a Certain Function

- Mathematics
- 2017

We discuss a character of quantum algorithms. In fact, all of them determine the property of a certain function. The function under study must have the property $f(x) = f(-x)$ when $f(x)\neq 0$.

Well-structured program equivalence is highly undecidable

- Computer ScienceTOCL
- 2012

This work introduces the construction of program equivalence, which returns the value ⊤ precisely when two given programs are equivalent on halting computations, and shows that virtually any variant of propositional dynamic logic has a Π11-hard validity problem if it can express even just the equivalence of well-structured programs with the empty program skip.

The Very True Theoretical Ultimate Algorithm for Quantum Computers

- Physics
- 2019

The quantum circuit gives us the ability to determine a perfect property of f(x), namely, $f(x)$.

Complementing deterministic tree-walking automata

- Computer ScienceInf. Process. Lett.
- 2006

Around the Pcp Theorem

- History
- 1997

jeev Arora, from Princeton, was the guest speaker. The participants thus had a unique occasion to hear about what is arguably the most spectacular result in the history of computational complexity…

Ultimate Algorithm for Quantum Computers

- Computer Science
- 2019

A novel parallel computation is proposed, even though today's algorithm methodology for quantum computing, for all of the combinations of values in variables of a logical function, and positively introduces a Boolean algebra here.

Büchi, Lindenbaum, Tarski: A Program Analysis Appetizer

- Computer ScienceIJCAI
- 2016

A research programme is described to establish precise, mathematical correspondences between these approaches to automata-theoretic and deductive proofs and to develop new analyzers using these results.

Quantum Circuits for Toom-Cook Multiplication

- Computer SciencePhysical Review A
- 2018

By analysing the recursive tree structure of the algorithm, a bound on the count of Toffoli gates and qubits is obtained and the asymptotic bounds are superior to the prior implementations of multiplier circuits using schoolbook and Karatsuba algorithms.

## References

SHOWING 1-2 OF 2 REFERENCES

Data Structures and Algorithms

- Computer ScienceUndergraduate Texts in Computer Science
- 1997

Object-oriented purists may view this book as one on object-based programming, using object-oriented analysis and design with implementation in Ada 95, and the approach transcends the specifics in any particular programming language.

Structure and Interpetation of Computer Programs

- Structure and Interpetation of Computer Programs
- 1985