Reset Words Research Articles

RESETting Timed Machines

Many real-time applications enable RESET to account for all kinds of unexpected problems, or to accommodate for a users’ want of restarting. Additionally, some software testing techniques must allow for resetting timed-Implementations Under Test (t-IUT). Dedicated internal logic is probably the most common of solutions for accomplishing such tasks. There are situations, however, where such a privilege doesn’t exist; thus, it cannot be built upon. Testing pre-engineered timed-IUTs is one such case. In this paper we wish to present an algorithm for the direct generation of timed RESET sequences from the timed-IUT specification, such that it should be optimal w.r.t. to execution time.

Optimum Frame Synchronization for OFDM Systems

Orthogonal frequency division multiplexing has emerged as a promising air interface scheme for wireless broadband communications. For OFDM systems, frame synchronization has received much attention in the literature, though simple correlators are still widely used in real systems. In this letter, we present the analytical expression of the optimal frame synchronizer for OFDM systems. Frame synchronization is posed as a maximum a posterioriprobability estimation. We show that the resulting frame synchronizer consists of a correlation term and a correction term. The correction term accounts for the random data surrounding a synchronization word. Numerical results show the performance gain of the proposed frame synchronizer over a correlation scheme.

Experiments on Synchronizing Automata

This work is motivated by the ˇ Cerny Conjecture - an old unsolved problem in the automata theory. We describe the results of the experiments on synchronizing automata, which have led us to two interesting results. The first one is that the size of an automaton al- phabet may play an important role in the issue of synchronization: we have found a 5-state automaton over a 3-letter alphabet which attains the upper bound from the ˇ Cerny Conjecture, while there is no such automaton (except ˇ Cerny automaton C5) over a binary alphabet. The second result emerging from the experiments is a theorem describing the dependencies between the automaton structure S expressed in terms of the so-called merging system and the maximal length of all minimal synchronizing words for automata of type S.

Emergent Slot Synchronization in Wireless Networks

This paper presents a biologically inspired approach for distributed slot synchronization in wireless networks. This is facilitated by modifying and extending a synchronization model based on the theory of pulse-coupled oscillators. The proposed Meshed Emergent Firefly Synchronization (MEMFIS) multiplexes synchronization words with data packets and adapts local clocks upon the reception of synchronization words from neighboring nodes. In this way, a dedicated synchronization phase is mitigated, as a network-wide slot structure emerges seamlessly over time as nodes exchange data packets. Simulation results demonstrate that synchronization is accomplished regardless of the arbitrary initial situation. There is no need for the selection of master nodes, as all nodes cooperate in a completely self-organized manner to achieve slot synchrony. Moreover, the algorithm is shown to scale with the number of nodes, works in meshed networks, and is robust against interference and collisions in dense networks.

Synchronizing random automata

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications Conjecture that any synchronizing automaton with n states has a reset word of length (n - 1)(2) was made by. Cerny in 1964. Notwithstanding the numerous attempts made by various researchers this conjecture hasn't been definitively proven yet. In this paper we study a random automaton that is sampled uniformly at random from the set of all automata with n states and m(n) letters. We show that for m(n) > 18 ln n any random automaton is synchronizing with high probability. For m(n) > n(beta), beta > 1/2 we also show that any random automaton with high probability satisfies the. Cerny conjecture.

Quantum finite-depth memory channels: Case study

We analyze the depth of the memory of quantum memory channels generated by a fixed unitary transformation describing the interaction between the principal system and internal degrees of freedom of the process device. We investigate the simplest case of a qubit memory channel with a two-level memory system. In particular, we explicitly characterize all interactions for which the memory depth is finite. We show that the memory effects are either infinite, or they disappear after at most two uses of the channel. Memory channels of finite depth can be to some extent controlled and manipulated by so-called reset sequences. We show that actions separated by the sequences of inputs of the length of the memory depth are independent and constitute memoryless channels.

Glenn Research Center quantum communicator receiver design and development

We investigate, design, and develop a prototype real-time synchronous receiver for the second-generation quantum communicator recently developed at the National Aeronautics and Space Administration (NASA) Glenn Research Center. This communication system exploits the temporal coincidences between simultaneously fired low-power laser sources to communicate at power levels several orders of magnitude less than what is currently achievable through classical means, with the ultimate goal of creating ultra-low-power microsize optical communications and sensing devices. The proposed receiver uses a unique adaptation of the early-late gate method for symbol synchronization and a newly identified 31-bit synchronization word for frame synchronization. This receiver, implemented in a field-programmable gate array (FPGA), also provides a number of significant additional features over the existing non-real-time experimental receiver, such as real-time bit error rate (BER) statistics collection and display, and recovery and display of embedded textual information. It also exhibits an indefinite run time and statistics collection.

Burst mode synchronization of QPSK on AWGN channels using kurtosis

This paper explores the use of kurtosis in synchronizing with a QPSK burst transmission. The start and end of the burst are a priori unknown and are detected without the use of pilot signals. After frame level synchronization, signal level synchronization is performed. The symbol timing, carrier frequency and carrier phase are recovered without the assistance of known symbols or synchronization words in the data stream, i.e. totally blind synchronization. The performance of frame, symbol and carrier synchronization algorithms is evaluated through computer simulations.

Biologically Inspired Intercellular Slot Synchronization

The present article develops a decentralized interbase station slot synchronization algorithm suitable for cellular mobile communication systems. The proposed cellular firefly synchronization (CelFSync) algorithm is derived from the theory of pulse-coupled oscillators, common to describe synchronization phenomena in biological systems, such as the spontaneous synchronization of fireflies. In order to maintain synchronization among base stations (BSs), even when there is no direct link between adjacent BSs, some selected user terminals (UTs) participate in the network synchronization process. Synchronization emerges by exchanging two distinct synchronization words, one transmitted by BSs and the other by active UTs, without any a priori assumption on the initial timing misalignments of BSs and UTs. In large-scale networks with inter-BS site distances up to a few kilometers, propagation delays severely affect the attainable timing accuracy of CelFSync. We show that by an appropriate combination of CelFSync with the timing advance procedure, which aligns uplink transmission of UTs to arrive simultaneously at the BS, a timing accuracy within a fraction of the inter-BS propagation delay is retained.

Synchronizing finite automata with short reset words

Finding synchronizing sequences for finite automata is a very important problem in many practical applications (part orienters in industry, reset problem in biocomputing theory, network issues, etc.). Problem of finding the shortest synchronizing sequence is NP-hard, so polynomial algorithms probably can work only as heuristic ones. In this paper we propose two versions of polynomial algorithms which work better than well-known Eppstein’s greedy algorithm and it is modification, a cycle algorithm, introduced by Trahtman.

A series of slowly synchronizing automata with a zero state over a small alphabet

For each integer n ⩾ 8 , we construct an n-state synchronizing automation with a zero state and only 2 input letters such that the minimum length of reset words for the automaton is n 2 + 6 n - 16 4 .

Robust multiple description image coding over wireless networks based on wavelet tree coding, error resilient entropy coding, and error concealment

In this paper, we propose an integrated robust multiple description coding (MDC) scheme for compressed still images over error-prone channels with both packet loss and random bit errors. Multiple descriptions are first generated independently by using multiple description scalar quantizer (MDSQ). To achieve an excellent error resilient capability for each description, multiple bitstreams are then generated based on wavelet trees along the spatial orientations. The spatial orientation trees in the wavelet domain are individually encoded using SPIHT. Error propagation is thus limited within each bitstreams. However, synchronization words are usually needed to avoid error propagation across multiple independent bitstreams. In order to maintain high compression efficiency robust synchronization, we adopt error resilient entropy coding (EREC) to re-organize these variable-length bitstreams into fixed-length data slots before multiplexing and transmission. Therefore, the synchronization of the start of each bitstream can be automatically obtained at the receiver. Finally, to alleviate the devastating image degradation resulted from errors in the beginning of the bitstreams, we propose an error concealment technique to both constrain the EREC/MDC decoding and post-process the decoded wavelet coefficients. With analysis and experimental results, we have demonstrated how each of these components has contributed to the overall robustness of the proposed transmission of compressed images over wireless channels.

Synchronizing and Collapsing Words

A word w over a finite alphabet Σ is called k-collapsing if for each finite deterministic automaton \(\mathcal{A} = \langle Q, \Sigma, \delta \rangle\) the inequality \(|\delta(Q,w)| \leq |Q|-k\) holds provided that \(|\delta(Q, \upsilon)| \leq |Q|-k\) for some word \(\upsilon\), depending on \({\mathcal{A}}\) . A word over the alphabet Σ is called k-synchronizing if it is a reset word for all synchronizing automata with k + 1 states and input alphabet Σ. The aim of this work is to give the motivations of the interest in these words and to provide an overview of some results in this area.

Algorithms for media

Falmagne recently introduced the concept of a medium, a combinatorial object encompassing hyperplane arrangements, topological orderings, acyclic orientations, and many other familiar structures. We find efficient solutions for several algorithmic problems on media: finding short reset sequences, shortest paths, testing whether a medium has a closed orientation, and listing the states of a medium given a black-box description.

Synchronizing automata with a letter of deficiency 2

We present two infinite series of synchronizing automata with a letter of deficiency 2 whose shortest reset words are longer than those for synchronizing automata obtained by a straightforward modification of Černý’s construction.

The \v Cerný conjecture for aperiodic automata

A word w is called a synchronizing (recurrent, reset, directable) word of a deterministic finite automaton (DFA) if w brings all states of the automaton to some specific state; a DFA that has a synchronizing word is said to be synchronizable. Cerny conjectured in 1964 that every n-state synchronizable DFA possesses a synchronizing word of length at most (n-1)2. We consider automata with aperiodic transition monoid (such automata are called aperiodic). We show that every synchronizable n-state aperiodic DFA has a synchronizing word of length at most n(n-1)/2. Thus, for aperiodic automata as well as for automata accepting only star-free languages, the Cerny conjecture holds true.

Algorithms and architecture implementations of MIMO OFDM baseband receiver based on the SIMD DSP core

This letter presents a programmable single-chip architecture for Multi-Input and Multi-Output (MIMO) OFDM baseband receiver. The architecture comprises a Single Instruction Multiple Data (SIMD) DSP core and three coprocessors that are used for synchronization, FFT and channel decoder. In this MIMO OFDM system, the Zero Correlation Zone (ZCZ) code is used as the synchronization word preamble of packet in the physical layer in order to avoid the interference from other transmitting antennas. Furthermore, a simple channel estimation algorithm is proposed which is appropriate for the SIMD DSP computation.

Notable trends concerning the synchronization of graphs and automata

A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Cerny had found in 1964 a sequence of n-state complete DFA with shortest synchronizing word of length (n− 1). He had conjectured that it is an upper bound for the length of the shortest synchronizing word for any n-state complete DFA. This simply looking conjecture is now one of the most longstanding open problems in the theory of finite automata. Moreover, the examples of DFA with shortest synchronizing word of length (n − 1) are relatively rare. To the Cerny sequence were added in all examples of Cerny, Piricka and Rosenauerova (1971), of Kari (2001) and of Roman (2004). An effective program for search of automata with minimal reset word of relatively great length has studied all automata of size n ≤ 10 for q = 2 (q size of alphabet) and of size n ≤ 7 for q ≤ 4. There are no contradictory examples for the Cerny conjecture in this class of automata. Moreover, the program does not find new examples of DFA with reset word of length (n−1)2 for automata with n > 4 as well as for q > 3. New examples of DFA with shortest synchronizing word of length (n − 1) were found only for n = 3, 4 and for q = 2, 3. And what is more, the examples with minimal length of reset word disappear even for values near the Cerny bound (n− 1) with growth of the size of the automaton as well as of the size of the alphabet. The gap between (n − 1) and the nearest of the minimal lengths of reset word appears for n = 6. The following table displays this interesting trend for the length of minimal reset words less than (n− 1).

Development of processor cores for digital consumer appliances

AbstractEmbedded processors are increasingly being used in digital consumer appliances such as cellular phones, digital still/video cameras, and car navigation systems. They must therefore deliver high performance within a reasonable area and power consumption level, and be flexible to meet a wide range of requirements for various applications. In this paper, we introduce our latest processor core SH‐X developed under the above background. The low‐power version of the SH‐X core achieves 360 MIPS with a power of 80 mW resulting in the high power‐performance ratio of 4500 MIPS/W. The standard version achieves 720 MIPS with a power of 250 mW, 2.8 GFLOPS, and 36M polygons/s graphics performance. The leak currents in the resume standby and U‐standby modes are 100 and 10µA, respectively. The resume standby mode can return the status before the standby in only 3 ms, while the U‐standby mode requires reset sequence to restart. © 2006 Wiley Periodicals, Inc. Syst Comp Jpn, 37(3): 10–19, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20450

On sequential frame synchronization in AWGN channels

We present a framework for the analysis of frame synchronization based on synchronization words (SWs), where the detection is based on the following sequential algorithm. The received samples are observed over a window of length equal to the SW; over this window, a metric (e.g., correlation) is computed; an SW is declared if the computed metric is greater than a proper threshold, otherwise the observation window is time-shifted one sample. We assume a Gaussian channel, antipodal signaling, equally distributed data symbols, and coherent detection, where soft values are provided to the frame synchronizer. We state the problem starting from the hypothesis testing theory, deriving the optimum metric [optimum likelihood ratio test (LRT)] according to the Neyman-Pearson lemma. When the data distribution is unknown, we design a simple and effective test based on the generalized LRT (GLRT). We also analyze the performance of the commonly used correlation metric, both with "hard" and "soft" values at the synchronizer input. We show that synchronization can be greatly improved by using the LRT and GLRT metrics instead of correlation and that, among correlation-based tests, sometimes hard correlation is better than soft correlation. The obtained closed-form expressions allow the derivation of the receiver operating characteristic (ROC) curves for the LRT and GLRT synchronizers, showing a remarkable gain with respect to synchronization based on correlation metric.