Computation Environments, An Interactive Semantics for Turing Machines (which P is not equal to NP considering it)

To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a universal processor and ii) a computist who uses the computability power of the universal processor to perform effective procedures. The notion of computation finds it meaning, for the computist, through his \underline{interaction} with the universal processor. We are interested in those computation environments which can be considered as alternative for the real computation environment that the human being is its computist. These computation environments must have two properties: 1- being physically plausible, and 2- being enough powerful. Based on Copeland' criteria for effective procedures, we define what a \emph{physically plausible} computation environment is. We construct two \emph{physically plausible} and \emph{enough powerful} computation environments: 1- the Turing computation environment, denoted by $E_T$, and 2- a persistently evolutionary computation environment, denoted by $E_e$, which persistently evolve in the course of executing the computations. We prove that the equality of complexity classes $\mathrm{P}$ and $\mathrm{NP}$ in the computation environment $E_e$ conflicts with the \underline{free will} of the computist. We provide an axiomatic system $\mathcal{T}$ for Turing computability and prove that ignoring just one of the axiom of $\mathcal{T}$, it would not be possible to derive $\mathrm{P=NP}$ from the rest of axioms. We prove that the computist who lives inside the environment $E_T$, can never be confident that whether he lives in a static environment or a persistently evolutionary one.Comment: 33 pages, interactive computation, P vs N

Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

The weak call-by-value λ-calculus is reasonable for both time and space

We study the weak call-by-value -calculus as a model for computational complexity theory and establish the natural measures for time and space Ð the number of beta-reduction steps and the size of the largest term in a computation Ð as reasonable measures with respect to the invariance thesis of Slot and van Emde Boas from 1984. More precisely, we show that, using those measures, Turing machines and the weak call-by-value -calculus can simulate each other within a polynomial overhead in time and a constant factor overhead in space for all computations terminating in (encodings of) łtruež or łfalsež. The simulation yields that standard complexity classes like , NP, PSPACE, or EXP can be defined solely in terms of the -calculus, but does not cover sublinear time or space. Note that our measures still have the well-known size explosion property, where the space measure of a computation can be exponentially bigger than its time measure. However, our result implies that this exponential gap disappears once complexity classes are considered instead of concrete computations. We consider this result a first step towards a solution for the long-standing open problem of whether the natural measures for time and space of the -calculus are reasonable. Our proof for the weak call-by-value -calculus is the first proof of reasonability (including both time and space) for a functional language based on natural measures and enables the formal verification of complexity-theoretic proofs concerning complexity classes, both on paper and in proof assistants. The proof idea relies on a hybrid of two simulation strategies of reductions in the weak call-by-value -calculus by Turing machines, both of which are insufficient if taken alone. The first strategy is the most naive one in the sense that a reduction sequence is simulated precisely as given by the reduction rules; in particular, all substitutions are executed immediately. This simulation runs within a constant overhead in space, but the overhead in time might be exponential. The second strategy is heap-based and relies on structure sharing, similar to existing compilers of eager functional languages. This strategy only has a polynomial overhead in time, but the space consumption might require an additional factor of log, which is essentially due to the size of the pointers required for this strategy. Our main contribution is the construction and verification of a space-aware interleaving of the two strategies, which is shown to yield both a constant overhead in space and a polynomial overhead in time

Topics in Programming Languages, a Philosophical Analysis through the case of Prolog

[EN]Programming languages seldom find proper anchorage in philosophy of logic, language and science. is more, philosophy of language seems to be restricted to natural languages and linguistics, and even philosophy of logic is rarely framed into programming languages topics. The logic programming paradigm and Prolog are, thus, the most adequate paradigm and programming language to work on this subject, combining natural language processing and linguistics, logic programming and constriction methodology on both algorithms and procedures, on an overall philosophizing declarative status. Not only this, but the dimension of the Fifth Generation Computer system related to strong Al wherein Prolog took a major role. and its historical frame in the very crucial dialectic between procedural and declarative paradigms, structuralist and empiricist biases, serves, in exemplar form, to treat straight ahead philosophy of logic, language and science in the contemporaneous age as well. In recounting Prolog's philosophical, mechanical and algorithmic harbingers, the opportunity is open to various routes. We herein shall exemplify some: - the mechanical-computational background explored by Pascal, Leibniz, Boole, Jacquard, Babbage, Konrad Zuse, until reaching to the ACE (Alan Turing) and EDVAC (von Neumann), offering the backbone in computer architecture, and the work of Turing, Church, Gödel, Kleene, von Neumann, Shannon, and others on computability, in parallel lines, throughly studied in detail, permit us to interpret ahead the evolving realm of programming languages. The proper line from lambda-calculus, to the Algol-family, the declarative and procedural split with the C language and Prolog, and the ensuing branching and programming languages explosion and further delimitation, are thereupon inspected as to relate them with the proper syntax, semantics and philosophical élan of logic programming and Prolog

An analysis of key generation efficiency of RSA cryptosystem in distributed environments

Thesis (Master)--Izmir Institute of Technology, Computer Engineering, Izmir, 2005Includes bibliographical references (leaves: 68)Text in English Abstract: Turkish and Englishix, 74 leavesAs the size of the communication through networks and especially through Internet grew, there became a huge need for securing these connections. The symmetric and asymmetric cryptosystems formed a good complementary approach for providing this security. While the asymmetric cryptosystems were a perfect solution for the distribution of the keys used by the communicating parties, they were very slow for the actual encryption and decryption of the data flowing between them. Therefore, the symmetric cryptosystems perfectly filled this space and were used for the encryption and decryption process once the session keys had been exchanged securely. Parallelism is a hot research topic area in many different fields and being used to deal with problems whose solutions take a considerable amount of time. Cryptography is no exception and, computer scientists have discovered that parallelism could certainly be used for making the algorithms for asymmetric cryptosystems go faster and the experimental results have shown a good promise so far. This thesis is based on the parallelization of a famous public-key algorithm, namely RSA

Aspects of emergent cyclicity in language and computation

This thesis has four parts, which correspond to the presentation and development of a theoretical framework for the study of cognitive capacities qua physical phenomena, and a case study of locality conditions over natural languages. Part I deals with computational considerations, setting the tone of the rest of the thesis, and introducing and defining critical concepts like ‘grammar’, ‘automaton’, and the relations between them . Fundamental questions concerning the place of formal language theory in linguistic inquiry, as well as the expressibility of linguistic and computational concepts in common terms, are raised in this part. Part II further explores the issues addressed in Part I with particular emphasis on how grammars are implemented by means of automata, and the properties of the formal languages that these automata generate. We will argue against the equation between effective computation and function-based computation, and introduce examples of computable procedures which are nevertheless impossible to capture using traditional function-based theories. The connection with cognition will be made in the light of dynamical frustrations: the irreconciliable tension between mutually incompatible tendencies that hold for a given dynamical system. We will provide arguments in favour of analyzing natural language as emerging from a tension between different systems (essentially, semantics and morpho-phonology) which impose orthogonal requirements over admissible outputs. The concept of level of organization or scale comes to the foreground here; and apparent contradictions and incommensurabilities between concepts and theories are revisited in a new light: that of dynamical nonlinear systems which are fundamentally frustrated. We will also characterize the computational system that emerges from such an architecture: the goal is to get a syntactic component which assigns the simplest possible structural description to sub-strings, in terms of its computational complexity. A system which can oscillate back and forth in the hierarchy of formal languages in assigning structural representations to local domains will be referred to as a computationally mixed system. Part III is where the really fun stuff starts. Field theory is introduced, and its applicability to neurocognitive phenomena is made explicit, with all due scale considerations. Physical and mathematical concepts are permanently interacting as we analyze phrase structure in terms of pseudo-fractals (in Mandelbrot’s sense) and define syntax as a (possibly unary) set of topological operations over completely Hausdorff (CH) ultrametric spaces. These operations, which makes field perturbations interfere, transform that initial completely Hausdorff ultrametric space into a metric, Hausdorff space with a weaker separation axiom. Syntax, in this proposal, is not ‘generative’ in any traditional sense –except the ‘fully explicit theory’ one-: rather, it partitions (technically, ‘parametrizes’) a topological space. Syntactic dependencies are defined as interferences between perturbations over a field, which reduce the total entropy of the system per cycles, at the cost of introducing further dimensions where attractors corresponding to interpretations for a phrase marker can be found. Part IV is a sample of what we can gain by further pursuing the physics of language approach, both in terms of empirical adequacy and theoretical elegance, not to mention the unlimited possibilities of interdisciplinary collaboration. In this section we set our focus on island phenomena as defined by Ross (1967), critically revisiting the most relevant literature on this topic, and establishing a typology of constructions that are strong islands, which cannot be violated. These constructions are particularly interesting because they limit the phase space of what is expressible via natural language, and thus reveal crucial aspects of its underlying dynamics. We will argue that a dynamically frustrated system which is characterized by displaying mixed computational dependencies can provide straightforward characterizations of cyclicity in terms of changes in dependencies in local domains