Semilinear Sets and Counter Machines: a Brief Survey

The idea of a finite automaton walking in a labyrinth goes back to Shannon /I/. In the last years this problem has been further investigated by D~pp /2/, M~ller /3/ and Budach /4/. DSpp posed the following question: Does there exist a finite initial automaton that finds a way out of every finite plane open labyrinth from any initial position and finally moves arbitrarily far away ? MGller and Budach gave negative answers to this question, where Budach used DSpp's original definitions, while MGller treated a graph-theoretical variant of D~pp's formulation. It is the aim of this note to show how some quite natural extensions of the computational power of the automaton (called mouse by Shannon) will affect the answer to this question. We allow the mouse to be either a finite automaton, a pushdown transducer, a linear bounded automaton, or a Turing machine. In the first to cases the answer to DSpp's question is negative, while an algorithmic solution for linear bounded automata exists, such that every open labyrinth may be mastered by such mice independent from the starting point. The negative answer in the case of pushdown transducers depends on the fact that there are labyrinths where pushdown transducers have the same computational power as finite automata (which may not master these labyrinths).

We consider non-self-embedding (NSE) context-free grammars as a representation of regular sets.We point out its advantages with respect to more classical representations by finite automata, in particular when considering the efficient realization of the rational operations. We give a characterization in terms of composition of regular grammars and state relationships between NSE grammars and push-down automata. Finally we show a polynomial algorithm to decide whether a context-free grammars is self-embedding or not.

Finite devices accepting infinite strings are the topic of several papers (see the recent surveys [4], [8] or [10], [11]). Most of these papers deal with finite automata. Thus finite automata as devices accepting infinite strings are wellunderstood. The situation is a little bit more involved if one considers more complicated accepting devices like, e.g., pushdown automata or Turing machines.

Coding is increasingly popular in schools around the world and is often taught by non-specialist teachers as an integrated task with other subject areas. In this article, we explore the relationship between computer science (CS) concepts and students’ multimodal expression in a coding animated narrative (CAN) task in the context of an integrated English-Technology unit of learning. Through this collective case study, we explore how CS concepts underpin semiotic elements of an animated narrative, analyse the factors that influence the extent to which students exercise those concepts, and reveal the tensions and opportunities that a CAN task may present for learning computer science concepts in regular, non-specialist, cross-curricular classrooms. The findings suggest that CAN tasks are unique in presenting opportunities for students to learn challenging CS concepts such as synchronisation and parallelism. At the same time, CAN tasks present tensions for teaching CS concepts in non-specialist classrooms, where student projects are often judged on their visual qualities. In such settings, procedural, rather than conceptual knowledge, may be a more efficient route to creative outcomes. It also means that drawing skills need to be prioritised. Role specialisation often led to better quality projects but at the expense of individual students’ conceptual development in computer science.

This manuscript contains the experimental realization of one instance of each automata in the theory of computation using chemistry and not using biochemistry. All automata are implemented in a 1-pot reactor. The Finite Automaton (FA) is represented by a precipitation reaction, the 1-stack Push Down Automaton (PDA) by a pH reaction network and the Turing machine (TM) by the Belousov-Zhabotinsky chemical reaction. The computation (consisting on recognizing if chemically transcribed abstract sequences belong to appropriate languages in the Chomsky hierarchy) is carried out by a chemical reaction recognizing the molecules and their order. Once the sequence is introduced in the reactor (very much as mRNA is introduced in the ribosome) the reaction does all the recognition without any need for external not strictly chemical help from reaction/diffusion set-ups or chemical gates. The result of the computation has a straightforward thermodynamic/information theory interpretation. These results are of interest for soft-robotics, chemically self-assembled systems, chemical neural networks, artificial intelligence and of course chemical computing (i. e., computing done by chemistry at molecular scales which translates to larger scales by the power of Avogadro's number) as well as natural computing and analog/digital computing.

It is known that there is no one-way, non-deterministic Pushdown Automaton (INPDA) which is a universal machine for the class of Finite Automata [6]. We will show that there is a two-way, deterministic Pushdown Automaton (2DPDA), U, which is a universal machine for the class of Finite Automata (FA). Our method will parallel Knuth and Bigelow's construction of a language which is not context sensitive but which is the acceptance set of some stack automaton [5], that is, we will construct a language which is not context-free, but which is accepted by a 2DPDA.

Subtree matching is an important problem in Computer Science on which a number of tasks, such as mechanical theorem proving, term-rewriting, symbolic computation and nonprocedural programming languages are based on. A systematic approach to the construction of subtree pattern matchers by deterministic pushdown automata, which read subject trees in prefix and postfix notation, is presented. The method is analogous to the construction of string pattern matchers: for a given pattern, a nondeterministic pushdown automaton is created and is then determinised. In addition, it is shown that the size of the resulting deterministic pushdown automata directly corresponds to the size of the existing string pattern matchers based on finite automata.

As a specific application of the material presented in Part I, this companion paper identifies VLSI layout strategies for realizing correlative encoded MSK-type Viterbi receivers. When the source symbols are correlatively encoded using a first-order polynomial, the appropriate Viterbi receiver takes the form of a cube-connected cycle (CCC) structure. Second-order encoding polynomials give rise to a new type of area-efficient VLSI structure which is a generalization of the CCC structure. The results are important from two perspectives: 1) Isomorphisms between certain concepts in theoretical computer science and digital communications are established, and 2) good practical VLSI layouts are generated, by a structured design methodology, which commercial silicon foundries can fabricate.

Chapter 17 Computation models and function algebras

Bisimilar linear systems

In general, a nondeterministic automaton or machine (for example a finite automaton, pushdown automaton or Turing machine) is called unambiguous if each input is accepted by at most one run or computation. Each deterministic automaton is obviously unambiguous. However, in many settings, unambiguous automata are more expressive or admit more succinct automata than deterministic models, while preserving some good algorithmic properties. The aim of this talk is to survey some classical and some more recent results on unambiguous finite automata over different kind of input structures, namely finite words, infinite words, finite trees, and infinite trees.

Many different deletion operations are investigated applied to languages accepted by one-way and two-way deterministic reversal-bounded multicounter machines as well as finite automata. Operations studied include the prefix, suffix, infix and outfix operations, as well as left and right quotient with languages from different families. It is often expected that language families defined from deterministic machines will not be closed under deletion operations. However, here, it is shown that one-way deterministic reversal-bounded multicounter languages are closed under right quotient with languages from many different language families; even those defined by nondeterministic machines such as the context-free languages, or languages accepted by nondeterministic pushdown machines augmented by any number of reversal-bounded counters. Also, it is shown that when starting with one-way deterministic machines with one counter that makes only one reversal, taking the left quotient with languages from many different language families, again including those defined by nondeterministic machines such as the context-free languages, yields only one-way deterministic reversal-bounded multicounter languages (by increasing the number of counters). However, if there are even just two more reversals on the counter, or a second 1-reversal-bounded counter, taking the left quotient (or even just the suffix operation) yields languages that can neither be accepted by deterministic reversal-bounded multicounter machines, nor by 2-way nondeterministic machines with one reversal-bounded counter. A number of other results with deletion operations are also shown.KeywordsRegular LanguageFinite AutomatonLanguage FamilyDeterministic Finite AutomatonInput TapeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This volume contains the proceedings of the 28th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), organized under the auspices of the Indian Association for Research in Computing Science (IARCS).

The main thesis of this chapter is that a dynamical viewpoint allows us to better understand some important foundational issues of computation theory. Effective procedures are traditionally studied from two different but complementary points of view. The first approach is concerned with individuating those numeric functions that are effectively calculable. This approach reached its systematization with the theory of the recursive functions (Gödel, Church Kleene).This theory is not directly concerned with computing devices or computations. Rather, the effective calculability of a recursive function is guaranteed by the algorithmic nature of its definition. In contrast, the second approach focuses on a family of abstract mechanisms, which are then typically used to compute or recognize numeric functions, sets of numbers, or numbers. These devices can be divided into two broad categories: automata or machines (Turing and Post), and systems of rules for symbol manipulation (Post). The mechanisms that have been studied include: a. Automata or Machines 1. gate-nets and McCulloch-Pitts nets 2. finite automata (Mealy and Moore machines) 3. push-down automata 4. stack automata 5. Turing machines 6. register machines 7. wang machines 8. cellular automata b. Systems of Rules 9. monogenic production systems in general 10. monogenic Post canonical systems 11. monogenic Post normal systems 12. tag systems. I call any device studied by computation theory a computational system. Computation theory is traditionally interested in studying the relations between each type of computational system and the others, and in establishing what class of numeric functions each type can compute. Accordingly one proves two kinds of theorem: (1) that systems of a given type emulate systems of another type (examples: Turing machines emulate register machines and cellular automata; cellular automata emulate Turing machines, etc.), and (2) that a certain type of system is complete relative to the class of the (partial) recursive functions or, in other words, that this type of system can compute all and only the (partial) recursive functions (examples of complete systems: Turing machines, register machines, cellular automata, tag systems, etc.). All different types of computational systems have much in common. Nevertheless, it is not at all clear exactly which properties these mechanisms share.

We introduce the concept of one-time nondeterminism as a new kind of limited nondeterminism for finite state machines and pushdown automata. Roughly speaking, one-time nondeterminism means that at the outset the computation is nondeterministic, but whenever it performs a guess, this guess is fixed for the rest of the computation. We characterize the computational power of one-time nondeterministic finite automata (OTNFAs) and one-time nondeterministic pushdown devices. Moreover, we study the descriptional complexity of these machines. For instance, we show that for an [Formula: see text]-state OTNFA with a sole nondeterministic state, that is nondeterministic for only one input symbol, [Formula: see text] states are sufficient and necessary in the worst case for an equivalent deterministic finite automaton. In case of pushdown automata, the conversion of a nondeterministic to a one-time nondeterministic as well as the conversion of a one-time nondeterministic to a deterministic one turn out to be non-recursive, that is, the trade-offs in size cannot be bounded by any recursive function.