PROGRESSIVE SOLUTIONS TO FSM EQUATIONS

Abstract. The equation solving problem is to derive the behavior of the unknown component X knowing the joint behavior of the other components (or the context) C and the specification of the overall system S. The component X can be derived by solving the Finite State Machine (FSM) equation C ◊ X ∼ S, where ◊ is the parallel composition operator and ∼ is the trace equivalence or the trace reduction relation. A solution X to an FSM equation is called progressive if for every external input sequence the composition C ◊ X does not fall into a livelock without an exit. In this paper, we formally define the notion of a progressive solution to a parallel FSM equation and present an algorithm that derives a largest progressive solution (if a progressive solution exists). In addition, we generalize the work to a system of FSM equations. Application examples are provided

Efficient Solution of Language Equations Using Partitioned Representations

A class of discrete event synthesis problems can be reduced to solving language equations f . X ⊆ S, where F is the fixed component and S the specification. Sequential synthesis deals with FSMs when the automata for F and S are prefix closed, and are naturally represented by multi-level networks with latches. For this special case, we present an efficient computation, using partitioned representations, of the most general prefix-closed solution of the above class of language equations. The transition and the output relations of the FSMs for F and S in their partitioned form are represented by the sets of output and next state functions of the corresponding networks. Experimentally, we show that using partitioned representations is much faster than using monolithic representations, as well as applicable to larger problem instances.Comment: Submitted on behalf of EDAA (http://www.edaa.com/

Can local single-pass methods solve any stationary Hamilton-Jacobi-Bellman equation?

The use of local single-pass methods (like, e.g., the Fast Marching method) has become popular in the solution of some Hamilton-Jacobi equations. The prototype of these equations is the eikonal equation, for which the methods can be applied saving CPU time and possibly memory allocation. Then, some natural questions arise: can local single-pass methods solve any Hamilton-Jacobi equation? If not, where the limit should be set? This paper tries to answer these questions. In order to give a complete picture, we present an overview of some fast methods available in literature and we briefly analyze their main features. We also introduce some numerical tools and provide several numerical tests which are intended to exhibit the limitations of the methods. We show that the construction of a local single-pass method for general Hamilton-Jacobi equations is very hard, if not impossible. Nevertheless, some special classes of problems can be actually solved, making local single-pass methods very useful from the practical point of view.Comment: 19 page

Extending fuzzy semantic model by advanced decision rules

This paper extends FSM, a recently proposed semantic data model that supports fuzziness, imprecision and uncertainty of real-world. More precisely, the paper proposes four new concepts, decisional grouping, inhibition, multiplicity and selection, which allows enhancing the modeling of real-world applications. It integrates these concepts in FSM by the definition of new decision rules

Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean field approach

We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchet-like transport mechanism arises through a symmetry-breaking noise-induced nonequilibrium phase transition. Numerical simulations of this system reveal amazing novel features such as negative zero-bias conductance and anomalous hysteresis, explained resorting to a strong-coupling analysis in the thermodynamic limit. Using an explicit mean-field approximation we explore the whole ordered phase finding a transition from anomalous to normal hysteresis inside this phase, estimating its locus and identifying (within this scheme) a mechanism whereby it takes place.Comment: RevTex, 21 pgs, 15 figures. Submited to Physical Review E (2000

Thermodynamics of sea ice phase composition revisited

Pure ice, brine and solid minerals are the main contributors to sea ice mass. Constitutional changes with salinity and temperature exert a fundamental control on sea ice physical, chemical, and biological properties. However, current estimation methods and model representations of the sea ice phase composition suffer from two limitations—in a context of poorly quantified uncertainties. First, salt minerals are neglected. Second, formulations are inconsistent with international standards, in particular with the International Thermodynamic Equation of Seawater (TEOS-10). To address these issues, we revisit the thermodynamics of the sea ice phase composition by confronting observations, theory, and the usual computation methods. We find remarkable agreement between observations and the Gibbs-Pitzer theory as implemented in FREZCHEM, both for brine salinity (RMSE=1.9g/kg) and liquid H2O mass fraction(RMSE=8.6g/kg). On this basis, we propose expanded sea ice phase composition equations including minerals, expressed in terms of International Temperature Scale 1990 temperature and absolute salinity,and valid down to the eutectic temperature (−36.2◦C). These equations precisely reproduce FREZCHEM,outcompeting currently used calculation techniques. We also suggest a modification of the TEOS-10seawater Gibbs function giving a liquidus curve consistent with observations down to the eutectic temperature without changing TEOS-10 inside its original validity range

Solving Parallel Equations with BALM-II

In this report we describe how to solve parallel language equations over regular languages / automata and finite state machines (FSMs), using the software package BALM-II. The original version of BALM could solve equations only with respect to synchronous composition; we extended the original code to solve also equations with respect to parallel composition, adding new commands and procedures. The new version of BALM is called BALM-II, of which this document provides a user's manual. Finally, as an important application, we describe how to synthesize protocol converters with BALM-II