Principal AFL

A (full) principal AFL is a (full) AFL generated by a single language, i.e., it is thesmallest (full) AFL containing the given language. In the present paper, a study is made of such AFL. First, an AFA (abstract family of acceptors) characterization of (full) principal AFL is given. From this result, many well-known families of AFL can be shown to be (full) principal AFL. Next, two representation theorems for each language in a (full) principal AFL are given. The first involves the generator and one application each of concatenation, star, intersection with a regular set, inverse homomorphism, and a special type of homomorphism. The second involves an a-transducer, the generator, and one application of concatenation and star. Finally, it is shown that if ℒ1 and ℒ2 are (full) principal AFL, then so are (a) the smallest (full) AFL containing {L1∩L2/L1 in ℒ1, L2 in ℒ2 and (b) the family obtained by substituting ε-free languages of ℒ2 into languages of ℒ1

Order dependency in the relational model

AbstractThe relational model is formally extended to include fixed orderings on attribute domains. A new constraint, called order dependency, is then introduced to incorporate semantic information involving these orderings. It is shown that this constraint can be applied to enhance the efficiency of an implemented database. The thrust of the paper is to study logical implication for order dependency. The main theoretical results consist in (i) introducing a formalism analogous to propositional calculus for analyzing order dependency, (ii) exhibiting a sound and complete set of inference rules for order dependency, and (iii) demonstrating that determining logical implication for order dependency is co-NP-complete. It is also shown that there are sets of order dependencies for which no Armstrong relations exist

Cohesion of object histories

AbstractIn an earlier paper, one of the authors introduced a record-based, algebraically-oriented, event-driven model for describing historical data for objects (here called “object histories”). The major construct in the model is a computation-tuple sequence scheme (CSS) which specifies the set of all possible “valid” object histories for the same type of object. The current paper considers the problem of combining the global information residing in a number of object histories in a distributed system. A suggested solution is in the form of an operation called “cohesion”, which is the analogue for object histories of join for relational databases.The basic question considered in this paper is the following: Given two sets I1 and l2 of object histories described by CSS T1 and T2, does there exist a CSS which describes the cohesion of l1 and l2? The answer is shown to be yes by constructing a specific CSS (called the “cohesion” of T1 and T2) from T1 and T2. The cohesion operation also turns out to be a useful tool for establishing some subsidiary results

A note on preservation of languages by transducers

An error in a previous paper is corrected. The rectified version involves pushdown transducers with accepting states instead of pushdown transducers. Some properties of pushdown transducers with accepting states are then noted

Subclasses of Presburger Arithmetic and the Weak EXP Hierarchy

It is shown that for any fixed $i>0$, the $\Sigma_{i+1}$-fragment of Presburger arithmetic, i.e., its restriction to $i+1$ quantifier alternations beginning with an existential quantifier, is complete for $\mathsf{\Sigma}^{\mathsf{EXP}}_{i}$, the $i$-th level of the weak EXP hierarchy, an analogue to the polynomial-time hierarchy residing between $\mathsf{NEXP}$ and $\mathsf{EXPSPACE}$. This result completes the computational complexity landscape for Presburger arithmetic, a line of research which dates back to the seminal work by Fischer & Rabin in 1974. Moreover, we apply some of the techniques developed in the proof of the lower bound in order to establish bounds on sets of naturals definable in the $\Sigma_1$-fragment of Presburger arithmetic: given a $\Sigma_1$-formula $\Phi(x)$, it is shown that the set of non-negative solutions is an ultimately periodic set whose period is at most doubly-exponential and that this bound is tight.Comment: 10 pages, 2 figure

Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages

For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular properties, in contrast to pure PDL. For regular, visibly pushdown and deterministic context-free languages, the separation of the respective PDLs can be proven by automata-theoretic techniques. However, these techniques introduce non-determinism on the automata side. As non-determinism is also the difference between DCFL and CFL, these techniques seem to be inappropriate to separate PDL[DCFL] from PDL[CFL]. Nevertheless, this separation is shown but for programs without test operators.Comment: In Proceedings GandALF 2011, arXiv:1106.081

D* Production in Deep Inelastic Scattering at HERA

This paper presents measurements of D^{*\pm} production in deep inelastic scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The data have been taken with the ZEUS detector at HERA. The decay channel $D^{*+}\to (D^0 \to K^- \pi^+) \pi^+$ (+ c.c.) has been used in the study. The $e^+p$ cross section for inclusive D^{*\pm} production with $5<Q^2<100 GeV^2$ and $y<0.7$ is 5.3 \pms 1.0 \pms 0.8 nb in the kinematic region {$1.3<p_T(D^{*\pm})<9.0$ GeV and $| \eta(D^{*\pm}) |<1.5$}. Differential cross sections as functions of p_T(D^{*\pm}), $\eta(D^{*\pm}), W$ and $Q^2$ are compared with next-to-leading order QCD calculations based on the photon-gluon fusion production mechanism. After an extrapolation of the cross section to the full kinematic region in p_T(D^{*\pm}) and $\eta$(D^{*\pm}), the charm contribution $F_2^{c\bar{c}}(x,Q^2)$ to the proton structure function is determined for Bjorken $x$ between 2 $\cdot$ 10$^{-4}$ and 5 $\cdot$ 10$^{-3}$.Comment: 17 pages including 4 figure