Jirí Wiedermann

SOFSEM 2000: Theory and Practice of Informatics

In protocol engineering area, conformance testing is a very important step. It tries to detect remaining errors after the verification step. The addition of time in system modeling, makes this step more complicated. This paper aims to give an overview on techniques for conformance testing of timed systems. It first describes some important models used to specify timed systems. Then, it shows the main techniques used for testing such systems. It will focus on two specific techniques. The first one is based on the extraction of a reduced number of test sequences, guided by a property required by any designer (called a test purpose). The second technique is based on the identification of some states on the implementation. The paper also shows how to experiment those test sequences on a real implementation and how to consider time in such an architecture.

Towards Algorithmic Explanation of Mind Evolution and Functioning

The cogitoid is a computational model of cognition introduced recently by the author. In cogitoids, knowledge is represented by a lattice of concepts and associations among them. From computational point of view any cogitoid is an interactive transducer whose transitions from one configuration into the next one depend on the history of past transitions. Cogitoids computational mechanism makes it possible for cogitoids to perform basic cognitive tasks such as abstraction formation, associative retrieval, causality learning, retrieval by causality, similarity-based behaviour, Pavlovian and operant conditioning, and reinforced learning. In addition, when a cogitoid is exposed to similar interaction as human brain during its existence, emergence of humanoid mind is to be expected. The respective development will subsequently feature emergence of various attentional mechanisms, essential living habits, development of abstract concepts, language understanding and acquisition, and, eventually, emergence of consciousness.

On the Power of Interactive Computing

In a number of recent studies the question has arisen whether the familiar Church-Turing thesis is still adequate to capture the powers and limitations of modern computational systems. In this presentation we review two developments that may lead to an extension of the classical Turing machine paradigm: interactiveness, and global computing.

Emergence of a Super-Turing Computational Potential in Artificial Living Systems

The computational potential of artificial living systems can be studied without knowing the algorithms that govern the behavior of such systems. What is needed is a formal model that neither overestimates nor underestimates their true computational power. Our basic model of a single organism will be the so-called cognitive automaton. It may be any device whose computational power is equivalent to a finite state automaton but which may work under a different scenario than standard automata. In the simplest case such a scenario involves a potentially infinite, unpredictable interaction of the model with an active or passive environment to which the model reacts by learning and adjusting its behaviour or even by purposefully modifying the environment in which it operates. One can also model the evolution of the respective systems caused by their architectural changes. An interesting example is offered by communities of cognitive automata. All the respective computational systems show the emergence of a computational power that is not present at the individual level. In all but trivial cases the resulting systems possess a super-Turing computing power. That is, the respective models cannot be simulated by a standard Turing machine and in principle they may solve non-computable tasks. The main tool for deriving the results is non-uniform computational complexity theory.

The Computational Limits to the Cognitive Power of the Neuroidal Tabula Rasa

The neuroidal tabula rasa (NTR) as a hypothetical device which is capable of performing tasks related to cognitive processes in the brain was introduced by L. G. Valiant in 1994. Neuroidal nets represent a computational model of the NTR. Their basic computational element is a kind of a programmable neuron called neuroid. Essentially it is a combination of a standard threshold element with a mechanism that allows modification of the neuroids computational behaviour. This is done by changing its state and the settings of its weights and of threshold in the course of computation. The computational power of an NTR crucially depends both on the functional properties of the underlying update mechanism that allows changing of neuroidal parameters and on the universe of allowable weights. We will define instances of neuroids for which the computational power of the respective finite-size NTR ranges from that of finite automata, through Turing machines, upto that of a certain restricted type of BSS machines that possess super-Turing computational power. The latter two results are surprising since similar results were known to hold only for certain kinds of analog neural networks.

Speeding-up Single-Tape Nondeterministic Computations by Single Alternation, with Separation Results

It is shown that for any well behaved function T(n), any single-tape nondeterministic Turing Machine of time complexity T(n) can be simulated by a single-tape Σ2-machine in time T(n)/logT(n). A similar result holds also for complementary, single-tape co-nondeter-ministic and II2machines. Consequently, NTIME1(T(n)) is strictly contained in Σ2-TIME1(T(n)), and analogously co-TIME1(T(n)) in II2-TIME1(T(n)), i.e., for single tape nondeterministic or co-nondeterministic machines adding of one more alternation leads to provably more powerful machines.

Simulating the mind: a gaunlet thrown to computer science

Understanding the activities of an animal or human mind in algorithmic terms seems to be about the greatest challenge offered to computer science by nature. In computer science, the respective cognitive information processing systems are studied within a new computational paradigm of cognitive computing recently introduced by L. Valiant [6]. This paradigm faces computer science with a number of new exciting research problems. Below we list dozen problems concerning cognitive systems in general and computational models of the brain or mind in particular.

A High Level Model of a Conscious Embodied Agent

We describe a simple yet cognitively powerful architecture of an embodied conscious agent. The architecture incorporates a mechanism for mining, representing, processing and exploiting semantic knowledge. This mechanism is based on two complementary internal world models which are built automatically. One model (based on artificial mirror neurons) is used for mining and capturing the “syntax” of the recognized part of the environment while the second one (based on neural nets) for its semantics. Jointly, the models support algorithmic processes underlying phenomena similar in important aspects to higher cognitive functions such as imitation learning and the development of communication, language, thinking and consciousness.

Speeding-Up Nondeterministic Single-Tape Off-Line Computations by One Alternation

It is shown that any nonderministic single-tape off-line Turing machine of time complexity T(n) can be speeded-up by one extra alternation by the factor log log T(n)/ √ log T(n), for any well-behaved function T(n). This leads to the separation NTIME1+I(T(n)) ⊂ σ 2 - TIME 1+I (T(n)) of the respective complexity classes. Analogous result holds also for the complementary classes co-NTIME1+I(T(n)) and π 2 - TIME1+I(T(n)). This is the first occasion where such separation results have been proved for a restricted type of multitape nondeterministic machines. For the general case of multitape nondeterministic machines similar results are not known to hold.

Parallel Machine Models: How They Are and Where Are They Going

The practice of parallel computing seems to be in a crises. The parallel processing has not become a common matter and the “second computer revolution” that should have been caused by the replacement of sequential computers by parallel ones is not to happen in near future. The only hope for overcoming the parallel computing crisis lays in the development of computational complexity theory. This offers a good opportunity to survey the respective results and trends in this theory and to discuss its reactions to the changing needs, both, in theory and practice of parallel computing. To provide an adequate answer to the current parallel computing crisis, building on the top of the respective theory, the focus in computer science is currently shifting from purely theoretically motivated problems also towards more practical ones, determined by the potential of hardware technologies today. As a result, computer science is looking for the “right” model of a parallel computer — namely for such a model that would present a reasonable design framework for algorithmic problem solving, would be elegant enough from a mathematical viewpoint and, last but not least, would allow for an efficient hardware realization. Despite the rather extensive effort, only partial success can be reported thus far.