Next-state Function Research Articles

Structure Theorems for Real-Time Variable Rate Coding With and Without Side Information

The output of a discrete Markov source is to be encoded instantaneously by a variable-rate encoder and decoded by a finite-state decoder. Our performance measure is a linear combination of the distortion and the instantaneous rate. Structure theorems, pertaining to the encoder and next-state functions, are derived for every given finite-state decoder, which can have access to side information.

Timing Optimization in Sequential Circuit by Exploiting Clock-Gating Logic

Clock gating is a popular technique for reducing power dissipation. In a circuit with clock gating, the clock signal can be shut off without changing the functionality under certain clock-gating conditions. In this article, we observe that the clock-gating conditions and the next-state function of a Flip-Flop (FF) are correlated and can be used for sequential circuit optimization. We also show that the implementation of the next-state function of any FF can be just an inverter if the clock signal is appropriately gated. By exploiting the flexibility between the clock-gating conditions and the next-state function, we propose an iterative optimization algorithm to improve the timing of sequential circuits. We present experimental results of a set of benchmark circuits with a timing improvement of 10.20% on average.

Reduction of the key space of the cipher A5/1 and invertibility of the next-state function for a stream generator

We study the stream ciphers that are based on the feedback shift registers. For a stream generator (in general form), we prove a theorem which allows us to equate the concept of invertibility of the next-state function and the concept of recurrency of the shift control function. Then we study a generator for the stream cipher A5/1 used in the GSM cellular telephone standard to ensure the confidentiality of conversations. For this generator, we count the number of states that can be obtained after t clock cycles from the initial states without predecessors and cannot be obtained in this way after the smaller number of cycles.We show how to exponentially reduce the key space of A5/1 while clocking. The results can be directly used in cryptanalysis of A5/1.

ON GUESS AND DETERMINE ANALYSIS OF RABBIT

Rabbit is a stream cipher proposed by M. Boesgaard et al., and has been selected into the final portfolio after three evaluation phases of the ECRYPT Stream Cipher Project (eSTREAM). So far only a few papers studied its security besides a series of white papers by the designers of Rabbit. Recently we presented a new idea to evaluate the security of a word-oriented stream cipher algorithm from a smaller data granularity instead of its original data granularity and applied it successfully to the stream cipher SOSEMANUK. In this work we apply the same idea to the Rabbit algorithm and analyze its security in resistance against the guess and determine attack from the view point of byte units. As a result, we present two new approaches of solving all xj,t+1' s and gj,t' s from the next-state function and the extraction scheme of Rabbit, whose complexities are 2166 and 2140.68 respectively, which are dramatically lower than those proposed by Lu et al. (2192 and 2174 resp.) at ISC 2008. Finally based on the above new results we propose a byte-based guess and determine attack on Rabbit, which only needs a small segment of known keystream to recover the whole internal state of Rabbit with time complexity 2242. Though the complexity of our attack is far higher than that of a brute force (2128), we believe that some new techniques adopted in this paper are of interest for future work on Rabbit.

Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models

AbstractOperational logic and bioinformatics models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes are proposed. Łukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Łukasiewicz Topos with an n-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.

유한체상의 순차디지털시스템 구성

This paper presents a method of constructing the sequential digital systems over finite fields. We assign all elements in finite fields to digit codes using mathematical properties of finite fields. Also, we discuss the operational characteristics and properties of the building block T-gate which is used to implement the sequential digital systems over finite fields. Then, we implemented sequential digital systems without feed-back. The sequential digital systems without feed-back is constructed as following steps. First, we assign the states in state-transition diagram to state digit codes, then obtain the state function and predecessor table which is explaining the relationship between present states and previous states. Next, we obtained the next-state function from state function and predecessor table. Finally we realize the circuit using T-gate and decoder. The proposed method is more efficiency and systematic than previous method.

A Study on Counter Design using Sequential Systems based on Synchronous Techniques

This paper presents a method of design the counter using sequential system based on synchronous techniques. For the design the counter, first of all, we derive switching algebras and their operations. Also, we obtain the next-state functions, flip-flop excitations and their input functions from the flip-flop. Then, we propose the algorithm which is a method of implementation of the synchronous sequential digital logic circuits. Finally, we apply proposed the sequential logic based on synchronous techniques to counter.

The computable kernel of Abstract State Machines

Abstract State Machines (ASMs) were introduced as “a computation model that is more powerful and more universal than standard computation models”, by Yuri Gurevich in 1985. ASMs gained much attention as a specification method. It is extremely flexible because any mathematical structure may serve as a state. Gurevich characterized the expressive power of ASMs in terms of intuitively convincing postulates. The core result of this paper shows that the next-state function M of an Abstract State Machine M can be described on a symbolic level, notwithstanding the generality of the model: The successor state M ( S ) of a state S is fully specified by the equivalence ∼ S induced by S on the terms over the signature of M . Consequently, M ( S ) is computable in case ∼ S is decidable. Furthermore, this result implies a notion of computability for general structures, e.g. for algorithms operating on real numbers.

Finding an internal state of RC4 stream cipher

The RC4 is a stream cipher widely deployed in software applications due to its simplicity and efficiency. The paper presents a cryptanalytic attack that employs the tree representation of this cipher and introduces an abstraction in the form of general conditions for managing the information about its internal state. In order to find the initial state, the tree of general conditions is searched applying the hill-climbing strategy. The complexity of this attack is lower than that of an exhaustive search. The attack is derived from a general cryptanalytic approach for a class of table-shuffling ciphers, whose next-state function permutes the table entries. Incorporating the general conditions in the existing backtracking algorithm, the estimated complexity of the cryptanalytic attack is decreased below the best published result but the RC4 still remains a quite secure cipher in practice.

Modeling protein dependency networks using CoCoA

In an interdisciplinary effort to model protein dependency networks, biologists measure signals from certain proteins within cells over a given interval of time. Using this time series data, the goal is to deduce protein dependency relationships. The mathematical challenges is to statistically measure correlations between given proteins over time in order to conjecture probable relationships. Biologists can then consider these relationships with more scrutiny, in order to confirm their conjectures. One algorithm for finding such relationships makes use of interpolation of the data to produce next-state functions for each protein and the Deegan-Packel Index of Power voting method to measure the strength of correlations between pairs of proteins. The algorithm was previously implemented, but limitations associated with the original language required the algorithm to be re-implemented in a more computationally efficient language. Because of the algebraic focus of the Computational Commutative Algebra language, or CoCoA, the algorithm was re-implemented in this language, and results have been produced much more efficiently. In this paper I discuss the algorithm, the CoCoA language, the implementation of the algorithm in CoCoA, and the quality of the results.

Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology.

The saturation algorithm for symbolic state-space exploration

We present various algorithms for generating the state space of an asynchronous system based on the use of multiway decision diagrams to encode sets and Kronecker operators on boolean matrices to encode the next-state function. The Kronecker encoding allows us to recognize and exploit the “locality of effect” that events might have on state variables. In turn, locality information suggests better iteration strategies aimed at minimizing peak memory consumption. In particular, we focus on the saturation strategy, which is completely different from traditional breadth-first symbolic approaches, and extend its applicability to models where the possible values of the state variables are not known a priori. The resulting algorithm merges “on-the-fly” explicit state-space generation of each submodel with symbolic state-space generation of the overall model.Each algorithm we present is implemented in our tool SmArT. This allows us to run fair and detailed comparisons between them on a suite of representative models. Saturation, in particular, is shown to be many orders of magnitude more efficient in terms of memory and time with respect to traditional methods.

Algebraic dependency models of protein signal transduction networks from time-series data

Signal transduction networks are crucial for inter- and intra-cellular signaling. Signals are often transmitted via covalent modification of protein structure, with phosphorylation/dephosphorylation as the primary example. In this paper, we apply a recently described method of computational algebra to the modeling of signaling networks, based on time-course protein modification data. Computational algebraic techniques are employed to construct next-state functions. A Monte Carlo method is used to approximate the Deegan–Packel Index of Power corresponding to the respective variables. The Deegan–Packel Index of Power is used to conjecture dependencies in the cellular signaling networks. We apply this method to two examples of protein modification time-course data available in the literature. These experiments identified protein carbonylation upon exposure of cells to sub-lethal concentrations of copper. We demonstrate that this method can identify protein dependencies that might correspond to regulatory mechanisms to shut down glycolysis in a reverse, step-wise fashion in response to copper-induced oxidative stress in yeast. These examples show that the computational algebra approach can identify dependencies that may outline signaling networks involved in the response of glycolytic enzymes to the oxidative stress caused by copper.

Specification and analysis of power-managed systems

Dynamic power management encompasses several techniques for reducing energy dissipation in electronic systems by selective slowdown or shutdown of components. We present a theoretical framework for explaining and classifying different approaches to power management. Within this framework, we model power-manageable components, workloads, and controllers as discrete-event systems (DESs). The structure of these DESs is specified in terms of physical states (representing operation modes) and events (triggering state transitions), while system behavior is specified in terms of next-event and next-state functions. In particular, nondeterministic next-event and next-state functions are modeled by conditional probability distributions, according to generalized semi-Markov processes (GSMPs). The modeling framework provides a general denotational model for system specification and a rigorous execution semantics that enables event-driven simulation. We introduce a modeling framework, built on top of MathWork's Simulink, supporting the specification and execution of our model. In particular, we present templates for the Simulink simulator to execute GSMP models, and we describe how to use such templates for specifying, analyzing, and optimizing dynamic power-managed systems. Finally, we demonstrate the expressive power and versatility of the proposed approach by using the modeling framework and the simulator for the analysis of representative real-life case studies, including the Intel Xscale processor architecture, a multitasking real-time system, and a sensor network.

Adaptive initial blocks for improving gradient-match and side-match vector quantization of images

The selection of initial blocks is one of the important issues in finite-state vector quantizers (FSVQs) for images. Conventional FSVQs use blocks located at fixed positions as initial blocks, which then are coded by the codewords in the super codebook. We propose an adaptive-initial-block (AIB) scheme to determine the initial blocks for gradient-match (GM) and side-match (SM) vector quantizers, which are two significant classes of FSVQs. According to the next-state functions used in GMVQs and SMVQs, the blocks with large boundary matching errors in original VQs are selected as the initial blocks. The error propagation effects can be reduced, and the coding performance is significantly improved. The simulation results show that the peak signal-to-noise ratios of coded images can be 2 dB higher than that of conventional GMVQs and SMVQs when the state codebook sizes are much smaller than that of the super codebook.

Implicit GSPN reachability set generation using decision diagrams

Implicit techniques for representing and generating the reachability set of a high-level model have become quite efficient. However, such techniques are usually restricted to models whose events have equal priority. Models containing events with differing classes of priority or complex priority structure, in particular models with immediate events, have thus been required to use less-efficient explicit reachability set generation techniques. In this paper, we present an efficient implicit technique, based on multi-valued decision diagram (MDD) representations for sets of states and matrix diagram representations for next-state functions, that can handle models with complex priority structure. We adapt an efficient Kronecker-based reachability set generation algorithm to work with matrix diagrams. If the model contains immediate events, the vanishing states can be eliminated either during generation, by manipulating the matrix diagram, or after generation, by manipulating the MDD. We apply both techniques to several models and give detailed experimental results.

Specification, Validation, and Synthesis of Email Agent Controllers: A Case Study in Function Rich Reactive System Design

With a few exceptions, previous formal methods for reactive system analysis have focused on finite state machines represented in terms of boolean states and boolean next-state functions. By contrast, in many reactive system domains requirements engineers and developers think in terms of complex data types and expressive next-state functions. Formal methods for reactive system design must be extended to meet their needs as well. I term a reactive system i>function rich if expressing its state, next-state function, or output function naturally requires this higher expressive power. ISAT, a prototype formal-methods based tool environment, is intended to assist in the creation and validation of function rich reactive systems. This paper describes a case study I have carried out using ISAT to design, validate, synthesize, and evolve controllers for the email agent components making up a novel spam-free email system that I deployed in a user trial in July 1999. The trial has been running since, with high availability, through several evolutionary specification changes and resulting software releases. The case study illustrates the use of a mix of validation techniques, from scenario simulation and coverage through static analysis and theorem proving, and discusses the value each technique adds. In addition to summarizing ISAT and the trial, this paper discusses tool requirements placed by the domain and task, the simple and powerful platform/controller/pure-functions software architecture of the components, and lessons learned.

An optimization of finite-state vector quantization for image compression

This paper focuses on the conditional histogram (CH) next-state function design used for the finite-state vector quantization (FSVQ) image compression approach. A new coding scheme is proposed which optimizes the performance of CH while ensuring the same reconstruction quality as that of the full-search VQ. The optimization is performed by determining for every input block the subcodebook size that minimizes the expected value of the number of bits in the compressed bit-flow. Two different algorithms are studied in order to ensure the best reconstruction. The proposed scheme is shown to give better results than classical FSVQ approaches. In fact, the proposed approach reveals the relationship between FSVQ and conditional entropy-coded VQ scheme.

ORBIT-PERIODS IN SECOND-ORDER FINITE-PRECISION DIGITAL FILTERS WITH OVERFLOW

The effect of n-bit precision on the orbit-periods of second-order lossless overflowing digital filters is discussed. It is observed that there are of the order of 2n orbits with periods O(2n), whereas in a random finite-state machine with the same number (2n)2 of states and with an invertible next-state function there are a few large orbits with periods O((2n)2). This behavior persists when the coefficient multiplication is replaced by a random mapping. This "randomized" model is readily understood and so provides a rough theory of the orbit-periods.

Stream cipher encryption of random access files

It is shown that synchronous stream ciphers based on keystream generators can be used for efficient and secure encryption/decryption of random access files if the underlying next-state function satisfies an associativity condition. In particular, secure designs based on combining different types of linearity in the next-state function are proposed.