On the Structure of (Weak) Inverses of an (Weakly) Invertible Finite Automaton

In this paper, we first give a method by which, for any weakly invertible finite automatonM with delay τ, the set of all weak inverse finite automata of M with delay τ can beconstructed. We then give a method by which, for any invertible one, all its inverses with delayτ can also be constructed.     

Structure of weakly invertible semi-input-memory finite automata with delay 2

Semi-input-memory finite automata,a kind of finite automata introduced by the author of this paper for studying error propagation,are a generalization of input-memory finite automata by appending an autonomous finite automaton component.This paper gives a characterization on the structure of weakly invertible semi-input-memory finite automata with delay 2 in which input alphabets and output alphabets have two elements and autonomous finite automata are cyclic.For the structure of feedforward inverse finite automata with delay 2,Zhu first gave a characterization;from a result on mutual invertibility of finite automata,the result mentioned above also leads to a different characterization on the structure of feedforward result mentioned above also leads to a different characterization on the structure of feedforward inverse finite automata with delay 2.     

Decomposing a kind of weakly invertible finite automata with delay 2

Some properties of a finite automaton composed of two weakly invertible finite automata with delay 1 are given,where each of those two automata has the output set of each state with the same size.And for a weakly invertible finite automaton M with delay 2 satisfying the properties mentioned in this paper,two weakly invertible finite automata with delay 1 are constructed such that M is equivalent to a sub-finite-automaton of the composition of those two.So a method to decompose this a kind of weakly invertible finite automate with delay 2 is presented.     

Structure of Weakly Invertible Semi-Input-Memory Finite Automata with Delay 1

Semi-input-memory finite automata,a kind of finite automata introduced by the first author of this paper for studying error propagation ,are a generalization of inputmemory finite automata ,by appending an autonomous finite automation component .In this paper,we give a characterization of the structure of weakly invertible semi-input-memory finite automata with delay 1,in which the state graph of each autonomous finite automation is cycle,From a result on mutual invertibility of finite automata obtained by th authors recently,it leads to a characerization of the structure of feedfoward inverse finite automata with delay 1.     

Semi-tensor product of matrices approach to reachability of finite automata with application to language recognition

This paper investigates the transition function and the reachability conditions of finite automata by using a semitensor product of matrices, which is a new powerful matrix analysis tool. The states and input symbols are first expressed in vector forms, then the transition function is described in an algebraic form. Using this algebraic representation, a sufficient and necessary condition of the reachability of any two states is proposed, based on which an algorithm is developed for discovering all the paths from one state to another. Furthermore, a mechanism is established to recognize the language acceptable by a finite automaton. Finally, illustrative examples show that the results/algorithms presented in this paper are suitable for both deterministic finite automata （DFA） and nondeterministic finite automata （NFA）.     

Input-trees of finite automata and application to cryptanalysis

In this paper,Weights of output set and of input set for finite automata are discussed.For a weakly invertible finite automaton,we prove that for states with minimal output weight,the distruibution of input sets is uniform.Then for a kind of compound finite automata,we give weights of output set and of input set explicitly,and a characterization of their input-trees.For finite automaton public key cryptosystems,of which automata in public keys belong to such a kind of compound finite automata,we evaluate search amounts of exhaust search algorithms in average case and in worse case for both encryption and signature,and success ful probabilities of stochastic search algorithms for both encryption and signature.In addition,a result on mutual invertibility of inite automata is also given.     

Approximation and universality of fuzzy Turing machines

Fuzzy Turing machines are the formal models of fuzzy algorithms or fuzzy computations. In this paper we give several different formulations of fuzzy Turing machine, which correspond to nondeterministic fuzzy Turing machine using max-＊ composition for some t-norm＊ （or NFTM＊, for short）, nondeterministic fuzzy Turing machine （or NFTM）, deterministic fuzzy Turing machine （or DFTM）, and multi-tape versions of fuzzy Turing machines. Some distinct results compared to those of ordinary Turing machines are obtained. First, it is shown that NFTM＊, NFTM, and DFTM are not necessarily equivalent in the power of recognizing fuzzy languages if the t-norm＊ does not satisfy finite generated condition, but are equivalent in the approximation sense. That is to say, we can approximate an NFTM＊ by some NFTM with any given accuracy; the related constructions are also presented. The level characterization of fuzzy recursively enumerable languages and fuzzy recursive languages are exploited by ordinary r.e. languages and recursive languages. Second, we show that universal fuzzy Turing machine exists in the approximated sense. There is a universal fuzzy Turing machine that can simulate any NFTM＊ on it with a given accuracy.     

Constructing finite automata with invertibility by transformation method

Ra,Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields.In a previous paper,the authors generalized Ra,Rb transformations to deal with nonlinear memory finite automata,and gave sufficient conditions for weak inverse and for weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automata satisfying one of these sufficient conditions were also given.This paper extends the concepts,methods and results to general finite automata,in which states consist of finite input history,finite output history and finite “inner state“ history.     

A Note on Non-Closure Property of Sublogarithmic Space-Bounded 1-Inkdot Alternating Pushdown Automata with Only Existential (Universal) States

1-inkdot alternating pushdown automaton is a slightly modified alternating pushdown automaton with the additional power of marking at most 1 tape-cell on the input （with an inkdot） once. This paper investigates the closure property of sublogarithmic space-bounded 1-inkdot alternating pushdown automata with only existential （universal） states, and shows, for example, that for any function L（n） such that L（n） ≥ log logn and L（n） = o（log n）, the class of sets accepted by weakly （strongly） L（n） space-bounded 1-inkdot two-way alternating pushdown automata with only existential （universal） states is not closed under concatenation with regular sets, length-preserving homomorphism, and Kleene closure.     

A framework for multi-robot motion planning from temporal logic specifications

We propose a framework for the coordination of a network of robots with respect to formal requirement specifications expressed in temporal logics.A regular tessellation is used to partition the space of interest into a union of disjoint regular and equal cells with finite facets,and each cell can only be occupied by a robot or an obstacle.Each robot is assumed to be equipped with a finite collection of continuous-time nonlinear closed-loop dynamics to be operated in.The robot is then modeled as a hybrid automaton for capturing the finitely many modes of operation for either staying within the current cell or reaching an adjacent cell through the corresponding facet.By taking the motion capabilities into account,a bisimilar discrete abstraction of the hybrid automaton can be constructed.Having the two systems bisimilar,all properties that are expressible in temporal logics such as Linear-time Temporal Logic,Computation Tree Logic,and μ -calculus can be preserved.Motion planning can then be performed at a discrete level by considering the parallel composition of discrete abstractions of the robots with a requirement specification given in a suitable temporal logic.The bisimilarity ensures that the discrete planning solutions are executable by the robots.For demonstration purpose,a finite automaton is used as the abstraction and the requirement specification is expressed in Computation Tree Logic.The model checker Cadence SMV is used to generate coordinated verified motion planning solutions.Two autonomous aerial robots are used to demonstrate how the proposed framework may be applied to solve coordinated motion planning problems.     

Generic Transformation from Weakly to Strongly Unforgeable Signatures

Current techniques for transforming unforgeable signature schemes （the forged message has never been signed） to strongly unforgeable ones （the forged message could have been signed） require supplementary components to be added onto the original key pairs of the schemes. In addition, some of them can only be applied to a certain type of signature schemes. In this paper, we propose a new generic transformation technique which converts any unforgeable signature scheme into a strongly unforgeable one without modifying any component in the original key pair. This makes our technique especially compatible for practical use. Our technique is based on strong one-time signature schemes. We show that they can be constructed efficiently from any one-time signature scheme that is based on one-way functions. The performance of our technique also compares favorably with that of current ones. Besides, it is shown in this paper that our transformation can further be applied to schemes satisfying only a weak variant of unforgeability without any further modification. Furthermore, our technique can also be used for constructing strongly unforgeable signature schemes in other cryptographic settings which include certificateless signature, identity-based signature, and several others. To the best of our knowledge, similar extent of versatility is not known to be supported by any of those comparable techniques. Finally and of independent interest, we show that our generic transformation technique can be modified to an on-line/off-line signature scheme, which possesses a very efficient signing process.     

Some Aspects of Synchronization of DFA

A word w is called synchronizing （recurrent, reset, directable） word of deterministic finite automata （DFA） if w brings all states of the automaton to a unique state. According to the famous conjecture of Cerny from 1964, every n-state synchronizing automaton possesses a synchronizing word of length at most （n - 1）2. The problem is still open. It will be proved that the Cerny conjecture holds good for synchronizing DFA with transition monoid having no involutions and for every n-state （n 〉 2） synchronizing DFA with transition monoid having only trivial subgroups the minimal length of synchronizing word is not greater than （n - 1）2/2. The last important class of DFA involved and studied by Schutzenberger is called aperiodic; its automata accept precisely star-free languages. Some properties of an arbitrary synchronizing DFA were established.     

FAPKC3: A New Finite Automaton PublicKey Cryptosystem

This paper deals with finite automaton public key cryptosystem and digital signatures.A new system FAPKC3 is proposed which can be used for encryption and implementing digital signatures as well.Some performances of a software implementation of FAPKC3 are presented and its security is discussed.     

Generating Conformance Tests for Nondeterministic Protocol Machines

We present a method of generating test cases from the software specifications which are modeled by nondeterministic finite state machines.It is applicable to both nondeterministic and deterministic finite state machines.When applied to deterministic machines,this method yields usually smaller test suites with full fault coverage than the existing methods that also assure full fault coverage.In particular,the proposed method can be used to test the control portion of software specified in the formal specification languages SDL or ESTELLE.     

Path Sensitization

For different delay models,the concept of sensitization can be very different.Traditonal concepts of sensitization cannot precisely describe circuit behavior when the input vectors change very fast.Using Boolean process aporoach,this paper presents a new definition of sensitization for arbitrary input waveforms.By this new concept it is found that if the inputs of a combinational circuit can change at any time,and each gate‘s delay varies within an interval (bounded gate delay model),then every path,which is not necessarily a single topological path,is sensitizable.From the experimental results it can be seen that,all nonsensitizable paths for traditional concepts actually can propagate transitions along them for some input waveforms.However,specified time between input transitions(STBIT) and minimum permissible pulse width(ε）are two major factors to make some paths non-sensitizable.     

A buffer planning algorithm for chip-level floorplanning

This paper studies the buffer planning problem for interconnect-centric floorplanning for nanometer technologies. The dead-spaces are the spaces left unused within a placement that are not held by any circuit block. In this paper, we proposed a buffer planning algorithm based on dead space redistribution to make good use of dead-spaces for buffer insertion. Associated with circuit blocks under topological representations, the dead space can be redistributed by moving freely some circuit blocks within their rooms in the placement. The total area and the topology of the placement keep unchanged while doing the dead space redistribution. The number of nets satisfying the delay constraint can be increased by redistributing the dead space all over the placement, which has been demonstrated by the experimental results. The increment of the number of nets that meet delay constraint is 9% on an average.     

Universal abstract consistency class and universal refutation

Refutation methods based on the resolution principle are generally applied to a (finite)set of sentences,which must have a series of pre-transformations(prenex normalization,Skolemization and conjunction normalization)before starting the refutation.In this paper,the authors first generalize the concept of abstract consistency class to the most general form-universal abstract consistency class,and prove its universal univfying principle.Then,based on the R-refutation,a universal refutation method is proposed and its soundness and completeness are proved by means of the universal unifying principle.This method can be applied directly to any finite set of wffs sithout preprocessing the wffs at all so that the refutation procedure is more natural.     

Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.     

Optimal bandwidth utilization of all-optical ring with a converter of degree 4

In many models of all-optical routing,a set of communication paths in a network is given,and a wavelength is to be assigned to each path so that paths sharing an edge receive different wavelengths .The goal is to assign as few wavelengths as possible,in order to use the optical bandwidth efficiently.If a node of a network contains a wavelength converter,any path that passes through this node may change its wavelength .Having converters at some of the nodes can reduce the mumber of wavelengths required for routing,This paper presents a wavelength converter with degree 4and gives a routing algorithm which shows that any routing with load L can be realized with L wavelengths when a node of an all-optical ring hosts such a wavelength converter.It is also proved that 4 is the minimum degree of the converter to reach the full utilization of the available wavelengths if only one mode of an all-optical ring hosts a converter.     

Lane of parallel through carry in ternary optical adder

At the present 50 to 100 microseconds are necessary for a liquid crystal to change its state from opacity to clarity; 1.14×10-5 microseconds are however proved to be enough for light to pass through a clarity liquid crystal device. Rooted from this great difference in time, an optical adder was constructed with parallel through carry lanes (PTCL) composed of liquid crystals. Because all carries in PTCL process in parallel, the carry delay in the ternary optical computer's adder is avoided. Eliminating the carry delay in adder of ternary optical computer by physical means, the PTCL is also applicable for other types of optical adders. Moreover a light diagram of the adder and one PTCL structure are provided.