Some textbooks of formal languages and automata theory implicitly state the structural equality of the binary n-dimensional de Bruijn graph and the state diagram of minimum state deterministic finite automaton which accepts regular language (0+1)*1(0+1)n-1. By introducing special finite automata whose accepting states are refined with two or more colors, we extend this fact to both k-ary versions. That is, we prove that k-ary n-dimensional de Brujin graph and the state diagram for minimum state deterministic colored finite automaton which accepts the (k-1)-tuple of the regular languages (0+1+…+k-1)*1(0+1+…+k-1)n-1,...,and(0+1+…+k-1)*(k-1)(0+1+…+k-1)n-1 are isomorphic for arbitrary k more than or equal to 2. We also investigate the properties of colored finite automata themselves and give computational complexity results on three decision problems concerning color unmixedness of nondeterminisitic ones.

A cooperating system of finite automata (CS-FA) has more than one finite automata (FA's) and an input tape. These FA's operate independently on the input tape and can communicate with each other on the same cell of the input tape. For each k ≥ 1, let L[CS-1DFA(k)] (L[CS-1UFA(k)]) be the class of sets accepted by CS-FA's with k one-way deterministic finite automata (alternating finite automata with only universal states). We show that L[CS-1DFA(k+1)] - L[CS-1UFA(k)] ≠ ∅ and L[CS-1UFA(2)] - ∪1≤k<∞L[CS-1DFA(k)] ≠ ∅.

Multi-pattern matching is a key technique for implementing network security applications such as Network Intrusion Detection/Protection Systems (NIDS/NIPSes) where every packet is inspected against tens of thousands of predefined attack signatures written in regular expressions (regexes). To this end, Deterministic Finite Automaton (DFA) is widely used for multi-regex matching, but existing DFA-based researches have claimed high throughput at an expense of extremely high memory cost, so fail to be employed in devices such as high-speed routers and embedded systems where the available memory is quite limited. In this paper, we propose a parallel architecture of DFA called Parallel DFA (PDFA) taking advantage of the large amount of concurrent flows to increase the throughput with nearly no extra memory cost. The basic idea is to selectively store the underlying DFA in memory modules that can be accessed in parallel. To explore its potential parallelism we intensively study DFA-split schemes from both state and transition points in this paper. The performance of our approach in both the average cases and the worst cases is analyzed, optimized and evaluated by numerical results. The evaluation shows that we obtain an average speedup of 100 times compared with traditional DFA-based matching approach.

Quantum random access coding (QRAC) is one of the basic tools in quantum computing. It uses a quantum state for encoding the sender's bit string so that the receiver can recover any single bit of the bit string with high probability. This article surveys recent developments of QRAC, with some concrete examples of QRAC using one quantum bit, and its applications, focusing on communication complexity and locally decodable codes.

Automated static timing analysis methods provide a safe but usually overestimated worst-case execution time (WCET) due to infeasible execution paths. In this paper, we propose a visual language, User Constraint Language (UCL), to obtain a tight WCET estimation. UCL provides intuitive visual notations with which users can easily specify various levels of flow information to characterize valid execution paths of a program. The user constraints specified in UCL are translated into finite automata. The combined automaton, constructed by a cross-production of the automata for program and user constraints, reflects the static structure and possible dynamic behavior of the program. It contains only the execution paths satisfying user constraints. A case study using part of a software program for satellite flight demonstrates the effectiveness of UCL and our approach.

For each positive integer r 1, a nondeterministic machine M is r path-bounded if for any input word x, there are r computation paths of M on x. This paper investigates the accepting powers of path-bounded one-way (simple) multihead nondeterministic finite automata. It is shown that for each k 2 and r 1, there is a language accepted by an (r + 1) path-bounded one-way nondeterministic k head finite automaton, but not accepted by any r path-bounded one-way nondeterministic k head finite automaton whether or not simple.

Inoue et al. introduced an automaton on a two-dimensional tape, which decides acceptance or rejection of an input tape by scanning the tape from various sides by various automata which move one way, and investigated the accepting power of such an automaton. This paper continues the investigation of this type of automata, especially, -type automata (obtained by combining four three-way two-dimensional deterministic finite automata (tr2-dfa's) in "or" fashion) and -type automata (obtained by combining four tr2-dfa's in "and" fashion). We first investigate a relationship between the accepting powers of -type automata and -type automata, and show that they are incomparable. Then, we investigate a hierarchy of the accepting powers based on the number of tr2-dfa's combined. Finally, we briefly describe a relationship between the accepting powers of automata obtained by combining three-way two-dimensional deterministic and nondeterministic finite automata.

The main purpose of this paper is to show that we can exploit the difference (l1-norm and l2-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It is shown that there is a finite language L which contains sentences of length up to O(nc+1) such that: (i) There is a one-way quantum finite automaton (qfa) of O(nc+4) states which recognizes L. (ii) However, if we try to simulate this qfa by a probabilistic finite automaton (pfa) using the same algorithm, then it needs Ω(n2c+4) states. It should be noted that we do not prove real lower bounds for pfa's but show that if pfa's and qfa's use exactly the same algorithm, then qfa's need much less states.

This paper is concerned with a comparative study of the accepting powers of deterministic, Las Vegas, self-verifying nondeterminisic, and nondeterministic (simple) multihead finite automata. We show that (1) for each k 2, one-way deterministic k-head (resp., simple k-head) finite automata are less powerful than one-way Las Vegas k-head (resp., simple k-head) finite automata, (2) there is a language accepted by a one-way self-verifying nondeterministic simple 2-head finite automaton, but not accepted by any one-way deterministic simple multihead finite automaton, (3) there is a language accepted by a one-way nondeterministic 2-head (resp., simple 2-head) finite automaton, but not accepted by any one-way self-verifying nondeterministic multihead (resp., simple multihead) finite automaton, (4) for each k 1, two-way Las Vegas k-head (resp., simple k-head) finite automata have the same accepting powers as two-way self-verifying nondeterministic k-head (resp., simple k-head) finite automata, and (5) two-way Las Vegas simple 2-head finite automata are more powerful than two-way deterministic simple 2-head finite automata.

An invertible length preserving transducer is called a weakly invertible finite automaton (WIFA for short). If the first letter of any input string of length τ + 1 is uniquely determined by the corresponding output string by a WIFA and its initial state, it is called a WIFA with delay τ. The composition of two WIFAs is the natural concatenation of them. The composition is also a WIFA whose delay is less than or equal to the sum of the delays of the two WIFAs. In this paper we derive various results on a decomposition of a WIFA into WIFAs with smaller delays. The motivation of this subject is from theoretical interests as well as an application to cryptosystems. In order to capture the essence of the decomposability problem, we concentrate on WIFAs such that their input alphabets and their output alphabets are identical. A WIFA with size n of the input and output alphabet is denoted by an n-WIFA. We prove that for any n > 1, there exists an n-WIFA with delay 2 which cannot be decomposed into two n-WIFAs with delay 1. A one-element logic memory cell is a special WIFA with delay 1, and it is called a delay unit. We show that for any prime number p, every strongly connected p-WIFA with delay 1 can be decomposed into a WIFA with delay 0 and a delay unit, and that any 2-WIFA can be decomposed into a WIFA wiht delay 0 and a sequence of k delay units if and only if every state of the 2-WIFA has delay k.

Over the last decade, research in the automatic synthesis and optimization of combinational logic has matured significantly; more recently, research has focused on sequential logic. Many of the paradigms for combinational logic have been extended and applied in the sequential domain. In addition, promising new directions for future research are being explored. In this paper, we survey some of the results of combinational synthesis and some recent results for sequential synthesis and then use these to view possible avenues for future sequential synthesis research. In particular we look at two related questions: deriving a set of permissible behaviors and using a minimizer to select the best behavior according to some optimization criteria. We examine these two issues in increasingly complex situations starting with a single-output function, and proceeding to a single multiple-output function, a network of single-output functions, a network of multiple-output functions, and then similar questions where function" is replaced by a finite state machine (FSM). We end with a discussion of a network of finite state machines and the problem of deriving the set of permissible FSM's and choosing a representative minimum one.

This paper introduces a new class of machines called multihead marker finite automata, and investigates how the number of markers affects its accepting power. Let HM{0}(i, j)(NHM{0}(i, j))denote the class of languages over a one-letter alphabet accepted by two-way deterministic (nondeterminstic) i-head finite automata with j markers. We show that HM{0} (i, j) HM{0}(i, j1) and NHM{0}(i, j) NHM{0}(i, j+1) for each i2, j0.

For each two positive integers r, s, let [1DCM(r)-Time(ns)] ([1NCM(r)-Time(ns)]) and [1DCM(r)-Space(ns)] ([1NCM(r)-Space(ns)]) be the classes of languages accepted in time ns and in space ns, respectively, by one-way deterministic (nondeterministic) r-counter machines. We show that for each X{D, N}, [1XCM(r)-Time(ns)][1XCM(r+1)-Time(ns)] and [1XCM(r)-Space(ns)][1XCM(r+1)-Space(ns)]. We also investigate the relationships between one-way multicounter machines and cooperating systems of one-way finite automata. In particular, it is shown that one-way (one-) counter machines and cooperating systems of two one-way finite automata are equivalent in accepting power.