Máquina de Turing Analógica para Ensino de Linguagens Formais e Autômatos

The article describes the development of a practical device for teachingin the area of Computer Theory. In the study, an adaptationof the Turing Machine is presented, using hardware and softwareintegration to interpret Formal Languages. Simulating an Automaton,sensors and motors are used to move the device head to the leftand right and to read and write the input tape. The developmentof the mechanism is described in two parts, the first includes thehardware that consists of the construction and adaptation of theTuring Machine, the second the implementation of the software andcommunication part between both. The developed device, allowsthe interpretation of a binary alphabet (0, 1), where an input word isaccepted, and as an output result, such device rejected or acceptedthe word.

Logarithmic Space Verifiers on NP-complete

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have f ailed. NP is the complexity class of languages defined b y p olynomial t ime v erifiers M su ch th at wh en th e in put is an el ement of the language with its certificate, then M outputs a string which belongs to a single language in P. Another major complexity classes are L and NL. The certificate-based definition of NL is based on logarithmic space Turing machine with an additional special read-once input tape: This is called a logarithmic space verifier. NL is the complexity class of languages defined by logarithmic space verifiers M s uch t hat when t he i nput i s a n e lement o f t he l anguage with i ts c ertificate, th en M outputs 1. To attack the P versus NP problem, the NP-completeness is a useful concept. We demonstrate there is an NP-complete language defined by a logarithmic space verifier M such that when the input is an element of the language with its certificate, then M outputs a s tring which belongs to a single language in L. In this way, we obtain if L is not equal to NL, then P = NP. In addition, we show that L is not equal to NL. Hence, we prove the complexity class P is equal to NP.

FINITE AUTOMATA WITH ADVICE TAPES

We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, demonstrate an infinite hierarchy of language classes recognized by automata with increasing advice lengths, and establish the relationships between this and the previously studied ways of providing advice to finite automata.

COMPUTATIONS AND DECIDABILITY OF ITERATIVE ARRAYS WITH RESTRICTED COMMUNICATION

Iterative arrays (IAs) are linear arrays of interconnected interacting finite state machines, where one distinguished one is equipped with a one-way read-only input tape. We investigate IAs operating in real time whose inter-cell communication is bounded by a constant number of bits not depending on the number of states. Their capabilities are considered in terms of syntactical pattern recognition. It is known [17] that such devices can recognize rather complicated sets of unary patterns with a minimum amount of communication, namely one-bit communication. Some examples are the sets {a2n | n ≥ 1}, {an2 | n ≥ 1}, and {ap | p is prime}. Here, we consider non-unary patterns and it turns out that the non-unary case is quite different. We present several real-time constructions for certain non-unary syntactical patterns. For example, the sets {anbn | n ≥ 1}, {anbncn | n ≥ 1}, {an(bn)m | n, m ≥ 1}, and {anbamb(ba)n·m | n, m ≥ 1} are recognized in real time by IAs. Moreover, it is shown that real-time one-bit IAs can, in some sense, add and multiply integer numbers. Furthermore, decidability questions of communication restricted IAs are dealt with. Due to the constructions provided, undecidability results can be derived. It turns out that emptiness is still not even semidecidable for one-bit IAs despite their restricted communication. Moreover, also the questions of finiteness, infiniteness, inclusion, and equivalence are non-semidecidable.

Von Neumann's Quintessential Message: Genotype + Ribotype = Phenotype

In this short article we argue that von Neumann's quintessential message with respect to self-replicating automata is genotype + ribotype = phenotype. Self-replication of his universal constructor occurs in analogy to nature: The description (genotype) written on the input tape is translated via a ribosome (ribotype) so as to create the offspring universal constructor (phenotype).

SAFE TURING MACHINES, GRZEGORCZYK CLASSES AND POLYTIME

We introduce a class of safe Turing machines which execute structured while, if-then- else programs and operate on stacks and on a read-only input tape. A hierarchy is obtained by taking as Si the class of all functions computed by programs of loop-depth i. The main result is that S1 equals Lintime and S2 equals Polytime while, for i≥3, we have that Si equals the i-th Grzegorczyk class. By adding to the language a non-deterministic construct choose we take S2 into a class equivalent to NP. This gives a syntactical characterization in a pure-machine model of the mentioned classes.

THE EFFECT OF INKDOTS FOR TWO-DIMENSIONAL AUTOMATA

Recently, related to the open problem of whether deterministic and nondeterministic space (especially lower-level) complexity classes are separated, the inkdot Turing machine was introduced. An inkdot machine is a conventional Turing machine capable of dropping an inkdot on a given input tape for a landmark, but not to pick it up nor further erase it. In this paper, we introduce a finite state version of the inkdot machine as a weak recognizer of the properties of digital pictures, rather than a Turing machine supplied with a one-dimensional working tape. We first investigate the sufficient spaces of three-way Turing machines to simulate two-dimensional inkdot finite automaton, as preliminary results. Next, we investigate the basic properties of two-dimensional inkdot automaton, i.e. the hierarchy based on the number of inkdots and the relationship of two-dimensional inkdot automata to other conventional two-dimensional automata. Finally, we investigate the recognizability of connected pictures of two-dimensional inkdot finite machines.