On the limits of refinement-testing for model-checking CSP

Refinement-checking, as embodied in tools like FDR, PAT and ProB, is a popular approach for model-checking refinement-closed predicates of CSP processes. We consider the limits of this approach to model-checking these kinds of predicates. By adopting Clarkson and Schneider’s hyperproperties framework, we show that every refinement-closed denotational predicate of finitely-nondeterministic, divergence-free CSP processes can be written as the conjunction of a safety predicate and the refinement-closure of a liveness predicate. We prove that every safety predicate is refinement-closed and that the safety predicates correspond precisely to the CSP refinement checks in finite linear observations models whose left-hand sides (i.e. specification processes) are independent of the systems to which they are applied. We then show that there exist important liveness predicates whose refinement-closures cannot be expressed as refinement checks in any finite linear observations model ${\mathcal{M}}$ , divergence-strict model ${\mathcal{M}^\Downarrow}$ or non-divergence-strict divergence-recording model ${\mathcal{M}^\#}$ , i.e. in any standard CSP model suitable for reasoning about the kinds of processes that FDR can handle, namely finitely-branching ones. These liveness predicates include liveness properties under intuitive fairness assumptions, branching-time liveness predicates and non-causation predicates for reasoning about authority. We conclude that alternative verification approaches, besides refinement-checking, currently under development for CSP should be further pursued.     

Two-step compensation of nonlinear systems

We study the problem of stabilization of nonlinear plants. We show that given a nonlinear plant P, if there exists a (nonlinear) compensator F, possibly unstable, which stabilizes P, then, with P₁: = P(I − F(− P))⁻¹, any C defined by C:= F + Q(I − P₁Q)⁻¹ for some finite-gain stable Q will stabilize P.     

Right,left characteristic sequences and column,row minimal indices of a singular pencil

For a general singular pencil sF — G?? ^m×n [s] the right, left characteristic sequences _r(F, G), _l(F, G) are defined and they are shown to be of the piecewise arithmetic progression type. The sets of column, row minimal indices ?_c(F, G), ?_r(F, G) are defined by a singular points analysis of _r(F, G), ?_l(F, G) respectively. Thus, ?_c(F, G), ?_r(F, G) emerge as numerical invariants of the ordered pair (F, G) and they may be computed by rank tests on Toeplitz matrices defined on (F, G).     

Special classes of separable Goppa codes with improved parameter estimates

We show that subclasses of q-ary separable Goppa codes Γ(L, G) with L = {α ∈ GF(q ^2ℓ): G(α) ∈ 0} and with special Goppa polynomials G(x) can be represented as a chain of equivalent and embedded codes. For all codes of the chain we obtain an improved bound for the dimension and find an exact value of the minimum distance. A chain of binary codes is considered as a particular case with specific properties.     

Definability, Canonical Models, Compactness for Finitary Coalgebraic Modal Logic

This paper studies coalgebras from the perspective of the finitary observations that can be made of their behaviours. Based on the terminal sequence, notions of finitary behaviours and finitary predicates are introduced. A category Beh_ω(T) of coalgebras with morphisms preserving finitary behaviours is defined.We then investigate definability and compactness for finitary coalgebraic modal logic, show that the final object in Beh_ω(T) generalises the notion of a canonical model in modal logic, and study the topology induced on a coalgebra by the finitary part of the terminal sequence.     

A metric for positional games

We define an extended real-valued metric, ρ, for positional games and prove that this class of games is a topological semigroup. We then show that two games are finitely separated iff they are path-connected and iff two closely related Conway games are equivalent. If two games are at a finite distance then this distance is bounded by the maximum difference of any two atoms found in the games. We may improve on this estimate when two games have the same form, as given by a form match. Finally, we show that if ρ(G,H)=∞ then for all X we have G+X H+X, a step towards proving cancellation for positional games.     

Eine Neue invariante für kontextfreie sprachen

Let G = (V, T, P, S) a c.f. grammar and F(V ? T) the free group generated by V ? T, (

(G) = F(V ? T/P is the quotient of F (V ? T) factorized by the relationsystem generated by P. We prove that (

(G) only depends on L(G) if G has no superflous variables. This means (fx107-1(G) is an invariant of grammar transformations which preserve the language. Each finitely representable group can be represented by a one sided liner grammar G as (

(G).In a straightforward manner one can compute finite basises for the Alexander-ideals of the groups (

(G. This ideals are finitely generated in an quotient of a Polynomring by a finitely generated ideal. Therefore this leads to effective computable necessary conditions for the equivalence of c.f. grammars.     

Stability of a Class of Differential Inclusions

Stability of differential inclusions F(x(t)) is studied by using minorant and majorant mappings F ^– and F ⁺, F ^–(x)F(x)F ⁺(x). Properties of F ^–,F ⁺ are developed in terms of partial orderings, with the condition that F ^–, F ⁺ are either heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, including the case of a single equilibrium point, and are illustrated by examples of control systems.     

Notes on wormhole existence in scalar-tensor and <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

Some recent papers have claimed the existence of static, spherically symmetric wormhole solutions to gravitational field equations in the absence of ghost (or phantom) degrees of freedom. We show that in some such cases the solutions in question are actually not of wormhole nature while in cases where a wormhole is obtained, the effective gravitational constant G _eff is negative in some region of space, i.e., the graviton becomes a ghost. In particular, it is confirmed that there are no vacuum wormhole solutions of the Brans-Dicke theory with zero potential and the coupling constant ω > −3/2, except for the case ω = 0; in the latter case, G _eff < 0 in the region beyond the throat. The same is true for wormhole solutions of F(R) gravity: special wormhole solutions are only possible if F(R) contains an extremum at which G _eff changes its sign.