Undecidability and Hierarchy Results for Parallel Communicating Finite Automata

In a similar way to DNA hybridization, antibodies which specifically recognize peptide sequences can be used for calculation [3,4]. In [4] the concept of peptide computing via peptide-antibody interaction is introduced and an algorithm to solve the satisfiability problem is given. In [3], (1) it is proved that peptide computing is computationally complete and (2) a method to solve two well-known NP-complete problems namely Hamiltonian path problem and exact cover by 3-set problem (a variation of set cover problem) using the interactions between peptides and antibodies is given. In our earlier paper [1], we proposed a theoretical model called as bindingblocking automata (BBA) for computing with peptide-antibody interactions. In [1] we define two types of transitions leftmost(l) and locally leftmost(ll) of BBA and prove that the acceptance power of multihead finite automata is sandwiched between the acceptance power of BBA in l and ll transitions. In this work we define a variant of binding-blocking automata called as string binding-blocking automata and analyze the acceptance power of the new model. The model of binding-blocking automaton can be informally said as a finite state automaton (reading a string of symbols at a time) with (1) blocking and unblocking functions and (2) priority relation in reading of symbols. Blocking and unblocking facilitates skipping 1 some symbols at some instant and reading it when it is necessary. In the sequel we state some results from [1,2] (1) for every BBA there exists an equivalent BBA without priority, (2) for every language accepted by BBA with l transition, there exists BBA with ll transitions accepting the same language, (3) for every language accepted by BBA with l transition there is an equivalent multi-head finite automata which accepts the same language and (4) for every language L accepted by a multi-head finite automaton there is a language L′ accepted by BBA such that L can be written in the form h−1(L′) where h is a homomorphism from L to L′. The basic model of the string binding-blocking automaton is very similar to a BBA but for the blocking and unblocking. Some string of symbols (starting form the head’s position) can be blocked from being read by the head. So only those symbols which are not already read and not blocked can be read by the head. The finite control of the automaton is divided into three sets of states namely blocking states, unblocking states and general reading states. A read symbol can not be read gain, but a blocked symbol can be unblocked and read.

Objective: The study of finite state automaton is an essential tool in machine learning and artificial intelligence. The class of rough finite state automaton captures the uncertainty using the rough transition map. The need to generalize this concept arises to adhere the dynamical behaviour of the system. Hence this paper focuses on defining non-homogeneous rough finite state automaton. Methodology: With the aid of Rough finite state automata we define the concept of non-homogeneous rough finite state automata. Findings: Non homogeneous Rough Finite State Automata (NRFSA) Mt is defined by a tuple (Q,Σ,δt,q0 (t),F(t)) The dynamical behaviour of any system can be expressed in terms of an information system at time t. This leads us to define non-homogeneous rough finite state automaton. For each time ‘t’ we generate lower approximation rough finite state automaton Mt_ and the upper approximation rough finite state automaton Mt- and the defined concepts are elaborated with suitable examples. The ordered pair , Mt=(M(t)-,M(t)-) is called as the non-homogeneous rough finite state automaton. Conclusion: Over all our study reveals the characterization of the system which changes its behaviour dynamically over a time ‘t’. Novelty: The novelty of the proposed article is that it clearly immense the system behaviour over a time ‘t’. Using this concept the possible and the definite transitions in the system can be calculated in any given time ‘t’.

Finite state automata are of fundamental importance in theory as well as applications in computer science. This dissertation presents several parallel algorithms for processing of them, including minimizing the number of states for a given finite state automaton, finding homing sequences for a given finite state automaton, converting a regular expression into an $\\varepsilon$-free nondeterministic finite automaton. Implementation of some algorithms, as well as their experimental results, are also given. For minimization of deterministic finite automata, we present a parallel algorithm and discuss its implementation on a practical parallel machine using data parallel and message passing paradigms. Its time complexity on a p processor EREW PRAM $(p\\le n)$ for inputs of size n is $O({n\\log\\sp2n\\over p}+\\log n\\ \\log p)$ uniformly on almost all instances. The work done by our algorithm is thus within a factor of $O(\\log n)$ of the best known sequential algorithm. The space used by our algorithm is linear in the input size. The actual resource requirements of our implementations are consistent with these estimates. For finding homing sequences of deterministic finite automata, we present both deterministic and randomized algorithms. Two randomized algorithms of time complexity $O(log\\sp2n)$ are given. One of the randomized algorithms produces a homing sequence of length $O(n\\ log\\sp2n)$ for almost all DFA's with n states. The deterministic algorithm is based on a well known sequential algorithm. The implementation of the deterministic parallel algorithm shows that it can handle randomly generated instances with millions of states, and all DFA's with thousands of states using currently available parallel machines. Finally, we present an efficient parallel algorithm for converting a regular expression into an $\\varepsilon$-free nondeterministic finite automaton. The resulting automaton is natural representation of a regular expression and has some important and practical uses in the document processing area. The time complexity of the algorithm is $O(\\log n)$ and the number of processors used is $O(n\\sp2).$

This chapter starts with a discussion of the algorithmic concepts of decidability, computability, and enumerability, introduces register machines and their programs as an exact model, and presents the proof of several undecidability results: of the valid first-order sentences, of the first-order sentences valid in finite structures (Trakhtenbrot's Theorem), and of first-order arithmetic. Furthermore, Gödel's incompleteness theorems are treated. Finally, the decidability of two theories is proved, of Presburger arithmetic and of the weak monadic theory of successor. For the latter some facts on finite automata are developed as far as needed.

Class temporal specification is a kind of important program specifications especially for object-oriented programs, which specifies that interface methods of a class should be called in a particular sequence. Currently, most existing approaches mine this kind of specifications based on finite state automaton. Observed that finite state automaton is a kind of deterministic models with inability to tolerate noise. In this paper, we propose to mine class temporal specifications relying on a probabilistic model extending from Markov chain. To the best of our knowledge, this is the first work of learning specifications from object-oriented programs dynamically based on probabilistic models. Different from similar works, our technique does not require annotating programs. Additionally, it learns specifications in an online mode, which can refine existing models continuously. Above all, we talk about problems regarding noise and connectivity of mined models and a strategy of computing thresholds is proposed to resolve them. To investigate our technique's feasibility and effectiveness, we implemented our technique in a prototype tool ISpecMiner and used it to conduct several experiments. Results of the experiments show that our technique can deal with noise effectively and useful specifications can be learned. Furthermore, our method of computing thresholds provides a strong assurance for mined models to be connected.

Yet another canonical nondeterministic automaton

In the last few decades, several techniques to randomly generate a deterministic finite automaton have been developed. These techniques have implications in the enumeration and random generation of automata of size n. One of the ways to generate a finite automaton is to generate a random tree and to complete it to a deterministic finite automaton, assuming that the tree will be the automaton's breadth-first spanning tree. In this paper we explore further this method, and the string representation of a tree, and use it to counting the number of automata having a tree as a breadth-first spanning subtrees. We introduce the notions of characteristic and difference sequence of a tree, and define the weight of a tree. We also present a recursive formula for this quantity in terms of the "derivative" of a tree. Finally, we analyze the implications of this formula in terms of exploring trees with the largest and smallest number of automata in the span of the tree and present simple applications for finding densities of subsets of DFAs.

We overview a series of our research on implementing finite automata in vitro and in vivo in the framework of DNA-based computing [1,2]. First, we employ the length-encoding technique proposed and presented in [3,4] to implement finite automata in test tube. In the length-encoding method, the states and state transition functions of a target finite automaton are effectively encoded into DNA sequences, a computation (accepting) process of finite automata is accomplished by self-assembly of encoded complementary DNA strands, and the acceptance of an input string is determined by the detection of a completely hybridized double-strand DNA. Second, we report our intensive in vitro experiments in which we have implemented and executed several finite-state automata in test tube. We have designed and developed practical laboratory protocols which combine several in vitro operations such as annealing, ligation, PCR, and streptavidin-biotin bonding to execute in vitro finite automata based on the length-encoding technique. We have carried laboratory experiments on various finite automata with 2 up to 6 states for several input strings. Third, we present a novel framework to develop a programmable and autonomous in vivo computer using Escherichia coli (E. coli), and implement in vivo finite-state automata based on the framework by employing the protein-synthesis mechanism of E. coli. We show some successful experiments to run an in vivo finite-state automaton on E. coli.KeywordsFinite AutomatonInput StringInput SymbollacZ Reporter GeneState Transition FunctionThese 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.

In order to improve validity and pertinence of strategies in robot soccer, this paper put forward a finite state automatons hierarchical decision model based on match state estimations. This model synthesizes and quantitates the information of state estimations and feedback of performing effects, establishes tactics conversion relationship based on finite state automatons, accordingly makes a tactic suiting current states. The simulations indicate that the decision model in this paper improves validity and pertinence of tactics to a great extent, enabling that whole abilities of attacking and defending for the soccer team attain corresponding melioration.

Functional dependency (FD) is one of the most analyzed integrity constraints for any data model. In the relational data model, FDs are defined in a natural way: the values of an attribute set Y depend on the values of another attribute set X, that is, "Y is a function of X". FDs are well studied and are widely used in normalization theory. XML functional dependencies (XFD) can be defined in different ways and no universally best definition has been proposed. They are defined by very intricate concepts, and they are mostly based upon XML elements described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. A semi-structured tuple is an ordered list of (attribute: value) pairs. We may think of a tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the nonterminal symbols. In this way, the sequence of the attribute names is the left side of a production rule used to accept the next terminal symbol, that is, the next value of the tuple. So the list of values forms the sentence and the list of attributes forms the dual sentence. In this paper, we introduce the notion of the extended tuple as a sentence from a regular language generated by a grammar where the nonterminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations (relations are instances). We then introduce the dual language, which generates the tuple types allowed to occur in extended relations. We define functional dependencies over extended relations. The syntax of functional dependencies will be given on the graph of the finite state automaton accepting the regular language. Using this model, we can also handle extended relations generated by recursive regular expressions. The implication problem of our class of dependencies is decidable and finitely axiomatizable by a version of the Chase algorithm performed on the graph of the associated finite state automaton.

In this paper, the hexapod robot model with symmetrical structure is established. Based on the hexapod robot's movement mechanism, the motion model about different fault joints of the leg is established. A strategy of fault-tolerant tripod gait is proposed. Finite state automata (FSA) is used to analyze the attitude transformation of the robot during normal operation and fault operation. Besides, the adjustment method of the fault tolerant triangle gait is analyzed when the different leg joints malfunction randomly. Finally, the effectiveness of this method is verified by physical platform.

Manufacturing and service sectors are evolving towards achieving a design of a systemically integrated product-service system (PSS). While there exist limitations, we propose an integrative design architecture and a design method for PSSs. For the integrated architecture, our study adopts the concepts of functions and affordances as fundamentals of PSS designs to achieve both the product and life-cycle related service design specifications. Also, finite state automata is applied to the modeling of the integrated PSS to add computations into the method. While the discussions on an automotive system shows the method's advancement as a PSS design tool, it is expected that this study will provide engineering designers and managers with a structured method that can be consistently applied through different PSSs life cycles.

In this paper, the similarity between a pair of text documents is measured by identifying three sets of words: words that exist in the first but not in the second, in the second but not in the first and those words that exist in both. Two deterministic finite automata are built to recognize the words of the two documents. These finite state automata are used to identify these three sets of words. An experimental study was conducted to present the proposed approach and to compare it with other peer text similarity measures: Jaccard and cosine distance. The proposed approach gave more reasonable results than Jaccard but more inflated than cosine distance approach.

Integrating control devices following different network architectures

At present, with the rapid development of software, software security is very more and more serious. In order to solve the software security problem, it is necessary to monitor the software behavior. Therefore, this paper studies the differences between the running states of the software, and finds out and quantifies the differences, which further monitors the software behavior in software security. This paper analyzes the topology structure algorithm of software behavior model and proposes FSM Diff algorithm based on finite state automaton. FSM Diff algorithm is more effective to select the key state nodes. Besides, experiment shows that FSM Diff algorithm is effective to select the key state nodes in the software running state diagram.