A Modular Algorithm for Computing Cohomologies of Lie Algebras and Superalgebras

The paper describes an improved algorithm for computing cohomologies of Lie (super)algebras. The original algorithm developed earlier by the author of this paper is based on the decomposition of the entire cochain complex into minimal subcomplexes. The suggested improvement consists in the replacement of the arithmetic of rational or integer numbers by a more efficient arithmetic of modular fields and the use of the relationship dim H ^k( _p) dimH ^k() between the dimensions of cohomologies over an arbitrary modular field _p = /p and the filed of rational numbers . This inequality allows us to rapidly find subcomplexes for which dimH ^k( _p) > 0 (the number of such subcomplexes is usually not great) using computations over an arbitrary _p and, then, carry out all required computations over in these subcomplexes.     

Crystalline Robots: Self-Reconfiguration with Compressible Unit Modules

We discuss a robotic system composed of Crystalline modules. Crystalline modules can aggregate together to form distributed robot systems. Crystalline modules can move relative to each other by expanding and contracting. This actuation mechanism permits automated shape metamorphosis. We describe the Crystalline module concept and show the basic motions that enable a Crystalline robot system to self-reconfigure. We present an algorithm for general self-reconfiguration and describe simulation experiments.     

Quantized innovations Kalman filter: stability and modification with scaling quantization

The stability of quantized innovations Kalman filtering (QIKF) is analyzed. In the analysis, the correlation between quantization errors and measurement noises is considered. By taking the quantization errors as a random perturbation in the observation system, the QIKF for the original system is equivalent to a Kalman-like filtering for the equivalent state-observation system. Thus, the estimate error covariance matrix of QIKF can be more exactly analyzed. The boundedness of the estimate error covariance matrix of QIKF is obtained under some weak conditions. The design of the number of quantized levels is discussed to guarantee the stability of QIKF. To overcome the instability and divergence of QIKF when the number of quantization levels is small, we propose a Kalman filter using scaling quantized innovations. Numerical simulations show the validity of the theorems and algorithms.     

A case study of Grid Computing and computer algebra: parallel Gröbner Bases and Characteristic Sets

This paper describes a parallel implementation of the Gröbner Bases algorithm and the Characteristic Sets method using a grid environment. The two algorithms, their parallelization, and grid-enabled implementations are presented. The performance of the implementations has been evaluated and the experiments have demonstrated considerable speedups.     

量化状态反馈网络化系统的稳定性分析

针对网络控制系统(Networked Control System,NCS)中普遍存在的有限带宽和信息量化问题,采用基于模型的控制策略,研究了量化状态反馈下一类网络控制系统的稳定性.分析了量化误差、更新时间、模型误差对系统稳定性的影响,并给出了系统模型状态、对象状态的稳定域范围.仿真结果表明了结论的正确性.     

Algebras with compatible quantale-enriched structures

Based on quantale-enriched category, we consider algebras with compatible quantale-enriched structures, which can be viewed as fuzzification of ordered algebraic structures. We mainly study groupoids and semigroups with compatible quantale-enriched structures from this viewpoint. Some basic concepts such as ideals, homomorphisms, residuated quantale-enriched groupoids are developed and some examples of them are given. Our approach gives a complement to the approach initiated by Rosenfeld to study fuzzy abstract algebra, and these two approaches are combined in the present paper to study fuzzy aspects of abstract algebra structures.     

Algebras, Coalgebras, Monads and Comonads

Whilst the relationship between initial algebras and monads is well-understood, the relationship between final coalgebras and comonads is less well explored. This paper shows that the problem is more subtle and that final coalgebras can just as easily form monads as comonads and dually, that initial algebras form both monads and comonads.In developing these theories we strive to provide them with an associated notion of syntax. In the case of initial algebras and monads this corresponds to the standard notion of algebraic theories consisting of signatures and equations: models of such algebraic theories are precisely the algebras of the representing monad. We attempt to emulate this result for the coalgebraic case by defining a notion cosignature and coequation and then proving the models of this syntax are precisely the coalgebras of the representing comonad.     

Conflict-Driven Satisfiability for Theory Combination: Lemmas,Modules, and Proofs

Journal of Automated Reasoning - Search-based satisfiability procedures try to build a model of the input formula by simultaneously proposing candidate models and deriving new formulae implied by...     

Computing with words

Computing with words is defined, in this paper, to be a symbolic generalization of fuzzy logic, which admits self-reference. It entails the randomization of declarative knowledge, which yields procedural knowledge. Such randomization can occur at two levels. First is termed weak randomization, which is essentially a domain-general pattern-matching operation. Second is termed strong randomization, which entails the application of one rule set to the semantics of another-possibly including itself. Strong randomization rests on top of weak randomization. Strong randomization is essentially a heuristic process. It is fully scalable, since it can in theory map out its own needed heuristics for evermore efficient search-including segmentation of the knowledge base. It is proven that strong learning must be knowledge-based, if effective. Computing with words does not preclude the use of predicate functions or procedural attachments. Also, the paradigm for computing with words does not directly compete with that for fuzzy logic. Rather, it serves to augment the utility of fuzzy logic through symbolic randomization. A countably infinite number of domain-specific logics or knowledge-based methods for randomization exist.     

Spectral Duality for Finitely Generated Nilpotent Minimum Algebras, with Applications

We establish a categorical duality for the finitely generatedLindenbaum-Tarski algebras of propositional nilpotent minimumlogic. The latter's conjunction is semantically interpretedby a left-continuous (but not continuous) triangular norm; implicationis obtained through residuation. Our duality allows one to transferto nilpotent minimum logic several known results about inutitionisticlogic with the prelinearity axiom (also called Gödel-Dummettlogic), mutatis mutandis. We give several such applications.     

Computing with Contexts

We investigate a representation of contexts, expressions with holes in them, that enables them to be meaningfully transformed, in particular -converted and -reduced. In particular we generalize the set of -expressions to include holes, and on these generalized entities define -reduction (i.e., substitution) and filling so that these operations preserve -congruence and commute. The theory is then applied to allow the encoding of reduction systems and operational semantics of call-by-value calculi enriched with control, imperative and concurrent features.     

Quantized stabilization of linear systems: complexity versus performance

Quantized feedback control has been receiving much attention in the control community in the past few years. Quantization is indeed a natural way to take into consideration in the control design the complexity constraints of the controller as well as the communication constraints in the information exchange between the controller and the plant. In this paper, we analyze the stabilization problem for discrete time linear systems with multidimensional state and one-dimensional input using quantized feedbacks with a memory structure, focusing on the tradeoff between complexity and performance. A quantized controller with memory is a dynamical system with a state space, a state updating map and an output map. The quantized controller complexity is modeled by means of three indexes. The first index L coincides with the number of the controller states. The second index is the number M of the possible values that the state updating map of the controller can take at each time. The third index is the number N of the possible values that the output map of the controller can take at each time. The index N corresponds also to the number of the possible control values that the controller can choose at each time. In this paper, the performance index is chosen to be the time T needed to shrink the state of the plant from a starting set to a target set. Finally, the contraction rate C, namely the ratio between the volumes of the starting and target sets, is introduced. We evaluate the relations between these parameters for various quantized stabilizers, with and without memory, and we make some comparisons. Then, we prove a number of results showing the intrinsic limitations of the quantized control. In particular, we show that, in order to obtain a control strategy which yields arbitrarily small values of T/lnC (requirement which can be interpreted as a weak form of the pole assignability property), we need to have that LN/lnC is big enough.     

Computing for Human Experience: Semantics-Empowered Sensors, Services, and Social Computing on the Ubiquitous Web

Computing for human experience will employ a suite of technologies to nondestructively and unobtrusively complement and enrich normal human activities, with minimal explicit concern or effort on the humans' part.     

Compositional Asymmetric Cooperations for Process Algebras with Probabilities,Priorities, and Time

The modeling and analysis experience with process algebras has shown the necessity of extending them with priority, probabilistic internal/external choice, and time in order to be able to faithfully model the behavior of real systems and capture the properties of interest. An important open problem in this scenario is how to obtain semantic compositionality in the presence of all these mechanisms, to allow for an efficient analysis.In this paper we argue that, when abandoning the classical nondeterministic setting by considering the mechanisms above, a natural solution is to break the symmetry of the roles of the processes participating in a synchronization. We accomplish this by distinguishing between master actions – the choice among which is carried out generatively according to their priorities/probabilities or exponentially distributed durations – and slave actions – the choice among which is carried out reactively according to their priorities/probabilities – and by imposing that a master action can synchronize with slave actions only.Technically speaking, in this paper we define a process algebra called EMPA_gr including probabilities, priorities, exponentially distributed durations, and the generative master-reactive slaves synchronization mechanism. Then, we prove that the synchronization mechanism in EMPA_gr is correct w.r.t. the novel cooperation structure model, we show that the Markovian bisimulation equivalence is a congruence for EMPA_gr, and we present a sound and complete axiomatization for finite terms.