Regular Trace Research Articles

SOME LIMIT DISTRIBUTIONS IN ANALYSIS OF ALGORITHMS FOR PROBLEMS ON TRACE LANGUAGES

We study the limit distribution of the sequence of random variables [Formula: see text] where, for each n, [Formula: see text] is the number of prefixes of a trace of length n chosen in a given free partially commutative monoid under the assumption that all representative strings of length n are equiprobable. We determine such a limit distribution for every free partially commutative monoid defined on a concurrent alphabet <Σ,C> such that the complementary relation Cc is transitive. We prove that if the complementary alphabet <Σ,Cc> has k connected components of equal size, then [Formula: see text] (suitably normalized) converges in distribution to a chi-square with k-1 degrees of freedom. On the other hand, if at least two connected components of <Σ,Cc> have a different number of vertices, then [Formula: see text] converges in distribution to a normal random variable. These probabilistic results yield the limit distribution of the time complexity of several algorithms for problems on trace languages, including algorithms for the Membership Problem of regular and context-free trace languages.

Laboratory quality control for a multicenter clinical trial: A report from the Growth Failure in Children with Renal Diseases Study

During the training-and-orientation session held at the beginning of the GFRD Study, and repeated when new centers joined the study, the necessity of uniform sample collection was emphasized. To avoid trace mineral contamination, collectors used all-plastic syringes and containers to collect blood for measurement of serum creatinine, magnesium, zinc, aluminum, and osteocalcin concentrations. A 5 ml blood sample is drawn from a fasting patient into a Peel-A-Way regular blood sampler (Peel-A-Way Scientific, South E1 Monte, Calif.) or trace mineral-free Vacutainer tubes (Becton Dickinson Vacutainer Systems, Rutherford, N.J.). The blood is allowed to clot at room temperature, and the clot is reamed with a disposable polyethylene fine-tip pipet. The tube is then centrifuged at 3000 rpm for 10 minutes and 0.5 ml of the serum is pipetted into each of five vials for the measurement of creatinine, zinc, magnesium, aluminum, and osteocalcin concentrations. The vials are frozen at 2 0 ~ C and mailed in dry ice by overnight courier to the GFRD Study Core Laboratory.

Regular trace formula and base change for $GL(n)$

Regular trace formula and base change for $GL(n)$

Characterizations of the decidability of some problems for regular trace languages

The decidability of the equivalence problem and the disjointness problem for regular trace languages is considered. By describing the structure of the independence relations involved, precise characterizations are given of those concurrency alphabets for which these problems are decidable. In fact, the first problem is decidable if and only if the independence relation is transitive, while the second problem is decidable if and only if the independence relation is a so-called transitive forest.

Membership problems for regular and context-free trace languages

Trace languages have been introduced in order to describe the behaviour of concurrent systems in the same way as usual formal languages do for sequential system. They can be defined as subsets of a free partially commutative monoid and a theory of trace languages can be developed, generalizing the usual formal languages theory. In this paper, the time complexity of membership problems for regular and context-free trace languages is investigated. It is proved that the membership problem for context free trace languages can be solved in time O ( BM ( n α )), where α is the dimension of the greatest clique of the concurrency relation C and BM ( n ) is the time required for multiplying two arbitrary n × n boolean matrices. For regular trace languages, our method gives an algorithm which requires O ( n α ) time. Finally, the uniform membership problem is shown to be NP-complete.

Regular Trace Formula and Base Change Lifting

Introduction. The Selberg trace formula has become a major tool in the study of automorphic forms on reductive groups. Although its underlying principle, of computing traces of representations by means of orbital integrals, is very simple, the standard expressions for this important formula are rather complicated; this makes applications hard to accomplish. The complexity of the expression for the formula may be due to the choice of truncation made in its proof. It would be advantageous to have a simple expression for the formula, at least for a set of test functions which is sufficiently large for applications. The possibility of its existence was suggested to us by some of Kazhdan's striking work on the trace formula (see, e.g., the density theorem of [Kl; Appendix], or the study of lifting in [K2]). Here we derive an asymptotic expression of this nature, in the simplest case of GL(2). For test functions with a component which is sufficiently with respect to all other components we obtain a simple, practical form of the trace formula. More precisely, if FU is a nonarchimedean local field and m 2 1 is an integer, we say that a locally constant function f, on Gu = GL(2, FU), which is supported on a compact-mod-center, is m-regular if it vanishes outside the open closed subset Sm = {zg-( ?)g; g in Gu; a, z in F,x with I a = 1 } (r denotes a uniformizer in F, x) of Gu, and its normalized orbital integral F(g ,fu) = A(g)4(g ,fu) is the characteristic function of Sm in G14. If F is a global field, u is a nonarchimedean place of F, and fu = ?, f, is a product over all places v ? u of F of smooth compactly supported mod-center functionsfv on Gv, such thatfv is the unit elementf v? of the Hecke algebra for almost all v, then we show that there exists mr0 = mo(fu) such that for any m 2r mo and m-regular functionfu = f (m), the regular test functionf = f (m) ? fu vanishes on the conjugacy classes in

On regular trace languages

We characterize here the free partially commutative monoids the regular sets of which form a Boolean algebra or are all unambiguous: these are, in both cases, the free products of free commutative monoids. This result has been established independently by other authors but the method used here is original. It is based on the properties of generalized automata on free products of monoids.

A logical characterization of observation equivalence

Brookes and Rounds (1983) showed that a finitary formal language (‘regular trace language’, or Reg-TL, for short) which allowed a certain kind of quantification using regular subsets of Σ ∗ was not strong enough to distinguish all pairs of observationally inequivalent synchronization trees. In the present paper we extend this result to show that there is no class C of subsets of Σ ∗ such that C -TL can distinguish all pairs of observationally inequivalent synchronization trees. We then give a characterization of observation equivalence in terms of an infinitary formal language S-TL( ω). This language is obtained as an extension of the language S-TL (‘singleton trace language’) of Hennessy and Milner by the addition of a connective of ω-conjunctions of formulas of finite bounded deoth.

Some Properties of Trace Languages

In this paper we present an application of nondeterministic multihead automata to the membership problem for trace languages. Here our result shows that regular and context-free trace languages are not very complicated. On the other hand, we make two simple observations which are the evidence that regular trace languages are very complicated from the algebraic point of view.

Concurrent Program Schemes and their Interpretations

Schemes of concurrent programs are considered. The result of a scheme is defined as a set of traces, where each trace is a partially ordered set of symbol occurrences. It is shown that to each scheme corresponds a set of equations determining the result of the scheme; it is shown how these equations can be solved and that the solutions of these equations are regular trace languages. Next, a notion of action systems is introduced; an action consists of its resources and its transformation. Some properties of action systems are shown. Interpretations of schemes are defined as mappings which assign actions to scheme symbols. Interpreted schemes can be regarded as concurrent programs. It is shown how the results of schemes can be lifted (via interpretations) to the results of programs. Some examples of applications of the described methods to prove concurrent programs correct are given.

Analysis of smooth type atmospheric waveforms

To resolve conflicting reports concerning smooth type waveforms, over 250 traces were extensively examined, as exemplifying wave-guide pulse dispersion. With very precise measurement, regular traces and those having various minor irregularities were distinguished. Over half the waveforms had regular traces and were directly explicable but analysis, accurate enough to give independent values of ionosphere height and propagation distance, was unattainable. Independent estimates of storm distances from a Sferics network suggested unexpected constancy of ionosphere height at 83 ± 2 km by day and night. Amplitude analysis gave identical average source spectra for day- and night-time waveforms and indicated unsuspectedly trivial variations of attenuation with frequency in the range 4–10 kc/s, and for the day to night transition.

A theory of spread F based on a scattering-screen model

To shed some light on the phenomenon of spread F, a thin scattering screen is postulated above the E region. The virtual height which is associated with a pulse radiated from the sounder, forward scattered by the screen and then reflected back to the sounder via the F region, is calculated. For frequencies appreciably larger than the penetration frequency, the minimum virtual height versus the operating frequency, on a linear scale, is a straight line, the slope of which depends on the height of the screen. As the height of the screen increases, the slope decreases. When the scattering screen is assumed at the level of reflection, the slope of the line coincides with the tangent from the origin to the regular vertical-incidence trace. Experimental ionograms are presented that fit with the suggested mechanism.

Galois Extensions in which Every Element with Regular Trace is a Normal Basis Element

Galois Extensions in which Every Element with Regular Trace is a Normal Basis Element

Galois extensions in which every element with regular trace is a normal basis element

Galois extensions in which every element with regular trace is a normal basis element