Interference automata

A two-way deterministic finite state automaton with one counter (2D1CA) is a fundamental computational model that has been examined in many different aspects since sixties, but we know little about its power in the case of unary languages. Up to our knowledge, the only known unary nonregular languages recognized by 2D1CAs are those formed by strings having exponential length, where the exponents form some trivial unary regular language. In this paper, we present some non-trivial subsets of these languages. By using the input head as a second counter, we present simulations of two-way deterministic finite automata with linearly bounded counters and linear–space Turing machines. We also show how a fixed-size quantum register can help to simplify some of these languages. Finally, we compare unary 2D1CAs with two–counter machines and provide some insights about the limits of their computational power.

Many difficult open problems in theoretical computer science center around nondeterminism. We study the fundamental problem of converting a given deterministic finite automaton (DFA) to a minimal nondeterministic finite automaton (NFA). Despite extensive work on finite automata, this fundamental problem has remained open. Recently, in [Ji91] we studied this problem and showed that this (and related) problems are computationally hard. Here we study the restriction of this problem to the case when the input DFA is over a one-letter alphabet. Even in this restricted case the problem is computationally hard even though our evidence of hardness is different from (and is weaker than) the standard ones such as NP-hardness. Let A → B denote the problem of converting a finite automaton of type A to a minimal finite automaton of type B. Our main result is that DFA → NFA, when the input is a unary cyclic DFA (a DFA whose graph is a simple cycle), is in NP but not in P unless NP ⊑ DTIME(nO(log n)). Our work was also motivated by the problem of finding structurally simple ‘normal forms’ of NFA's over a unary alphabet. We present some normal forms for minimal NFA's over a unary alphabet and present an application to lower bounds on the size complexity of an NFA. In fact, the normal form result is used in a nontrivial manner to show the NP membership result stated above.

Power of the interactive proof systems with verifiers modeled by semi-quantum two-way finite automata

This Paper presents a multimodal spectral metrics and Deterministic Finite Automata (DFA) in a manner to enhance the detection of spikes and seizures in epileptiform activity from Electroencephalograms (EEG). To develop robust classification rules for identifying epileptiform activity in the human brain the authors present a new methodology to connect their previous work where successful prediction of epileptiform activity was achieved through the use of DFA. The link between DFA seizure detection operating in the time-domain and frequency domain seizure detection has been a non-trivial task and this paper presents a means to link four power spectra metrics of rat EEG experiencing epilepsy seizures and previous work by the authors where the same rats experience seizures that the authors DFA algorithm identified the seizures. We propose a system that links 1) four power spectra metrics capable of detecting seizure activity with 2) Deterministic Finite Automata (DFA). It is a common goal for those skilled in the art of epilepsy prediction to create classifiers that are used to make rules and isolate characteristic events leading to an epileptic seizure. Herein, we present a means to link time and frequency domains using various spectral metrics and DFA to identify the electrographic onset of a seizure.

Many network security applications in today's networks are based on deep packet inspection, checking not only the header portion but also the payload portion of a packet. For example, traffic monitoring, layer-7 filtering, and network intrusion detection all require an accurate analysis of packet content in search for predefined patterns to identify specific classes of applications, viruses, attack signatures, etc. Regular expressions are often used to represent such patterns. They are implemented using finite automata, which take the payload of a packet as an input string. However, existing approaches, both non-deterministic finite automata (NFA) and deterministic finite automata (DFA), do not deal with compressed traffic, which becomes more and more popular in HTTP applications. In this paper, we propose an efficient algorithm for regular expression matching to implement deep packet inspection on compressed traffic. Based on the observations of DFA, we design a scheme to skip most of the matching process in the compressed parts of traffic. To the best of our knowledge, this is the first effort to design an efficient regular expression matching on compressed traffic. We evaluate our algorithm using rule sets provided by Snort, a popular open-source intrusion detection system. The evaluation results show that our approach can reduce the number of state access in the DFA significantly.

This paper is a continuation of the goal to connect power spectra and Deterministic Finite Automata (DFA) in a manner to enhance the detection of spikes and seizures in epileptiform activity from Electroencephalograms (EEG). The goal is to develop robust classification rules for identifying epileptiform activity in the human brain. This paper presents advancement using the author’s proprietary developed spectral analysis to link power spectra of rat EEGs experiencing epilepsy seizures with the authors DFA algorithm and their MATLAB spectral analysis. We present a system that links 1) power spectra of seizures, in sleep, spike and seizure states with 2) Deterministic Finite Automata (DFA). Combining power spectra with DFA to correctly predict and identify epileptiform activity (spikes) and epileptic seizures opens the door to creating classifiers for seizures. It is a common goal for those skilled in the art of epilepsy prediction to create classifiers to make rules and discretize events leading to an epileptic seizure. Herein we present a means to link time and frequency domain components from MATLAB and proprietary software to clinical epileptiform activity.

The finite automata are mathematical models for finite state systems. More general finite automaton is the nondeterministic finite automaton (NFA) that cannot be directly used. It is usually transformed to the deterministic finite automaton (DFA) that then runs in time O(n), where n is the size of the input text. We present two main approaches to practical implementation of DFA considering CPU cache. The first approach (represented by Table Driven and Hard Coded implementations) is suitable forautomata being run very frequently, typically having cycles. The other approach is suitable for a collection of automata from which various automata are retrieved and then run. This second kind of automata are expected to be cycle-free.

Angluin's L$^*$ algorithm learns the minimal deterministic finite automaton (DFA) of a regular language using membership and equivalence queries. Its probabilistic approximatively correct (PAC) version substitutes an equivalence query by numerous random membership queries to get a high level confidence to the answer. Thus it can be applied to any kind of device and may be viewed as an algorithm for synthesizing an automaton abstracting the behavior of the device based on observations. Here we are interested on how Angluin's PAC learning algorithm behaves for devices which are obtained from a DFA by introducing some noise. More precisely we study whether Angluin's algorithm reduces the noise and produces a DFA closer to the original one than the noisy device. We propose several ways to introduce the noise: (1) the noisy device inverts the classification of words w.r.t. the DFA with a small probability, (2) the noisy device modifies with a small probability the letters of the word before asking its classification w.r.t. the DFA, (3) the noisy device combines the classification of a word w.r.t. the DFA and its classification w.r.t. a counter automaton, and (4) the noisy DFA is obtained by a random process from two DFA such that the language of the first one is included in the second one. Then when a word is accepted (resp. rejected) by the first (resp. second) one, it is also accepted (resp. rejected) and in the remaining cases, it is accepted with probability 0.5. Our main experimental contributions consist in showing that: (1) Angluin's algorithm behaves well whenever the noisy device is produced by a random process, (2) but poorly with a structured noise, and, that (3) is able to eliminate pathological behaviours specified in a regular way. Theoretically, we show that randomness almost surely yields systems with non-recursively enumerable languages.

There is an increasing demand for network devices to perform deep packet inspection (DPI) in order to enhance network security. In DPI, the packet payload is compared against a set of predefined patterns that can be specified using regular expressions (regexes). It is well-known that mapping regexes to deterministic finite automaton (DFA) may suffer from the state explosion problem. Through observation, we attribute DFA explosion to the necessity of remembering matching history. In this paper, we investigate how to manage matching history efficiently and propose an extended DFA approach for regex matching called fcq-FA, which can make a memory size reduction of about 1,000 times with a fully automated approach. In fcq-FA, we use pipeline queues and counters to help record the matching history. Hence, state explosion caused by Kleene closure and length restriction can be completely avoided. Furthermore, it achieves a fully automated signature compilation with polynomial running time and space. The equivalence between fcq-FA and the traditional DFA is guaranteed by a strict theoretical proof, which means fcq-FA can process all the regexes supported by the traditional DFA.

In this paper, we analyze the problem of state minimization in a class of Finite State Automata called Two Start State Deterministic Finite State Automata (2-MDFAs). A 2-MDFA is similar to a deterministic finite state automaton (DFA), in that on a given input, each state has precisely one destination state; however, it differs from a DFA in that there are two start states. A string is accepted by a 2-MDFA if and only if there exists a transitional path from either start state to a finish state, on that string . Observe that 2-MDFAs provide a limited amount of non-determinism and hence investigating their properties from the perspective of state minimization is a worthwhile pursuit. In case of unbounded non-determinism, i.e., Non-deterministic finite state automata (NFAs), it is well-known that the state minimization problem is PSPACE-complete [Jiang and Ravikumar in Proceedings of the 18th International Colloquium on Automata, Languages and Programming, ICALP’91, Madrid, Spain, July 8–12, 1991] and further that such automata can be exponentially more succinct than DFAs [Meyer and Fischer in Proceedings of the 12th SWAT(Annual Symposium on switching and automata theory), pp 188-191, 1971]. Even in the case of 2-MDFAs, the minimization problem remains non-trivial; indeed, Malcher in Theor Comput Sci 327(3):375–390, 2004 shows that the corresponding decision problem is NP-complete. We focus on deriving approximability bounds for the state minimization problem in 2-MDFAs. Our main contribution in the current paper, is the design of an n -approximation algorithm for state minimization in 2-MDFAs, where n denotes the minimum number of states required to represent the input language as a 2-MDFA. We also present a proof that this bound is tight for our algorithm.

Computer Science and Engineering have given us the field of automata theory, one of the largest areas that is concerned with the efficiency of an algorithm in solving a problem on a computational model. Various classes of formal languages are represented using Chomsky hierarchy. These languages are described as a set of specific strings over a given alphabet and can be described using state or transition diagrams. The state/transition diagram for regular languages is called a finite automaton which is used in compiler design for recognition of tokens. Other applications of finite automata include pattern matching, speech and text processing, CPU machine operations, etc. The construction of finite automata is a complicated and challenging process as there is no fixed mathematical approach that exists for designing Deterministic Finite Automata (DFA) and handling the validations for acceptance or rejection of strings. Consequently, it is difficult to represent the DFA’s transition table and graph. Novel learners in the field of theoretical computer science often feel difficulty in designing of DFA The present paper proposes an algorithm for designing of deterministic finite automata (DFA) for a regular language with a given prefix. The proposed method further aims to simplify the lexical analysis process of compiler design.

Chapter 1 - Formal Requirements and Finite Automata Overview

Yet another canonical nondeterministic automaton

Deep Packet Inspection (DPI) systems have been becoming an important element in traffic measurement ever since port-based classification was deemed no longer appropriate, due to protocol tunneling and misuses of well-defined ports. Current DPI systems express application signatures using regular expressions and it is usual to perform pattern matching through the use of Finite Automaton (FA). Although DPI systems are essentially more accurate, they are also resource-intensive and do not scale well with link speeds. Looking to this area of interest, this paper proposes a novel Deterministic Finite Automaton, called Ranged Compressed Deterministic Finite Automaton (RCDFA), that compresses transitions without additional memory lookups. Experimental results show that RCDFA yields space savings of 97% over the original DFA and up to 93% better compression when compared to the DFA's state-of-the-art compression techniques.

[Formula: see text] is a binary coded unary regular language, if there exists a unary regular language [Formula: see text] such that [Formula: see text] is in [Formula: see text] if and only if the binary representation of [Formula: see text] is in [Formula: see text]. If a unary language [Formula: see text] is accepted by a minimal deterministic finite automaton (DFA) [Formula: see text] with [Formula: see text] states, then its binary coded version [Formula: see text] is regular and can be accepted by a DFA [Formula: see text] using at most [Formula: see text] states, but at least [Formula: see text] states. There are witness languages matching these upper and lower bounds exactly, for each [Formula: see text]. More precisely, if [Formula: see text] uses [Formula: see text] states in the initial segment and [Formula: see text] states in the loop, where [Formula: see text] is odd and [Formula: see text], then the minimal [Formula: see text] for [Formula: see text] consists of a preamble with at most [Formula: see text] but at least [Formula: see text] states, except for [Formula: see text] with no preamble, and a kernel with at most [Formula: see text] but at least [Formula: see text] states. Also these lower bounds are matched exactly by witness languages, for each [Formula: see text]. If the length of the loop is fixed, the size of the preamble is bounded by [Formula: see text]. The conversion in the opposite way is not always granted: there are binary regular languages the unary versions of which are not even context free. The conversion of a unary nondeterministic finite automaton (NFA) to a binary NFA uses [Formula: see text] states and introduces a binary version of Chrobak normal form.