A Characterization of Morphic Words with Polynomial Growth

A morphic word is obtained by iterating a morphism to generate an infinite word, and then applying a coding. We characterize morphic words with polynomial growth in terms of a new type of infinite word called a $\textit{zigzag word}$. A zigzag word is represented by an initial string, followed by a finite list of terms, each of which repeats for each $n \geq 1$ in one of three ways: it grows forward [$t(1)\ t(2)\ \dotsm\ t(n)]$, backward [$t(n)\ \dotsm\ t(2)\ t(1)$], or just occurs once [$t$]. Each term can recursively contain subterms with their own forward and backward repetitions. We show that an infinite word is morphic with growth $\Theta(n^k)$ iff it is a zigzag word of depth $k$. As corollaries, we obtain that the morphic words with growth $O(n)$ are exactly the ultimately periodic words, and the morphic words with growth $O(n^2)$ are exactly the multilinear words

On Infinite Words Determined by Indexed Languages

We characterize the infinite words determined by indexed languages. An infinite language $L$ determines an infinite word $\alpha$ if every string in $L$ is a prefix of $\alpha$. If $L$ is regular or context-free, it is known that $\alpha$ must be ultimately periodic. We show that if $L$ is an indexed language, then $\alpha$ is a morphic word, i.e., $\alpha$ can be generated by iterating a morphism under a coding. Since the other direction, that every morphic word is determined by some indexed language, also holds, this implies that the infinite words determined by indexed languages are exactly the morphic words. To obtain this result, we prove a new pumping lemma for the indexed languages, which may be of independent interest.Comment: Full version of paper accepted for publication at MFCS 201

The Tenth District economy: picking up the pace

The Tenth District economy improved overall during 1993 thanks to a booming construction sector and healthy growth in services. The district's gain was uneven, however, because other major sectors of the region's economy remained mixed. Economic performance also diverged considerably across the seven district states.> Smith reviews the district's economic performance in 1993 and explores the outlook for 1994. The district economy will probably improve slightly in 1994 as the national economy continues to strengthen. District manufacturing should improve somewhat, but construction may slacken from its recent vigorous pace. The district should not expect to gain additional strength from two of the region's key industries agriculture and energy. Overall, the district economy is expected to grow moderately in the year ahead.Federal Reserve District, 10th

The Tenth District's expanding service sector

The proliferation of service jobs in the nation has received much attention. While the manufacturing sector has suffered substantial job losses during the current business cycle, job growth in services has been brisk. Because the service sector comprises a diverse collection of service industries, there is considerable confusion about what kinds of jobs the service industries are creating and what factors will affect the outlook for the service sector.> In the Tenth District, service industry jobs have grown even faster than in the nation. As the service sector becomes a bigger share of the work force, its performance will increasingly influence the outlook for the region's economy. The service sector already employs more workers than any other economic sector in the district, yet little is known about the individual industries that make up this sector. Smith explores the dimensions of the district's service sector and considers the outlook for its key industries.Federal Reserve District, 10th ; Service industries

Tenth district survey of manufacturers

Manufacturing is a major force in the Tenth District economy, accounting for the largest share of output in the region and one of the largest shares of employment. Moreover, many manufacturing jobs are among the highest paying jobs in the district. Yet little information is available to track the performance of this major sector. Monthly employment data provide the most current information, but these data are only available with a considerable lag.> To provide up-to-date information about manufacturing conditions in the Tenth District, the Federal Reserve Bank of Kansas City has developed a quarterly survey of manufacturing plants. Smith provides background information for users of the manufacturing survey. Beginning in the fourth quarter of 1995, the survey results will be published in each issue of the bank's Regional Economic Digest.Federal Reserve District, 10th ; Manufactures

Tenth District economic developments

The Tenth District economy grew at a moderate pace during 1996. The district economy expanded vigorously in early 1996 but slowed as the year progressed. Tight labor markets in many parts of the region appeared to limit job growth, particularly in the large trade and services sectors. A slumping cattle industry also curbed overall growth in parts of the district. Nonetheless, construction continued to post healthy gains, energy activity improved somewhat, and manufacturing across the region remained stable.> Smith reviews the district's economic performance in 1996 and explores the outlook for 1997. In the year ahead, the district economy will probably continue to grow moderately, about equal to the 1996 pace. Tight labor markets will continue to constrain growth in many parts of the district. District manufacturing will likely remain stable, while trade and services continue to expand at a more sustainable, moderate pace than in previous years. Construction activity may moderate, but the farm economy is expected to improve somewhat, reflecting relatively strong prices and an improving outlook for the cattle industry.Federal Reserve District, 10th

Undecidability and Finite Automata

Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to prove the undecidability of a related problem about k-automatic sets of rational numbers

Aerodynamic characteristics of the modified 40- by 80-foot wind tunnel as measured in a 1/50th-scale model

The aerodynamic characteristics of the 40- by 80-Foot Wind Tunnel at Ames Research Center were measured by using a 1/50th-scale facility. The model was configured to closely simulate the features of the full-scale facility when it became operational in 1986. The items measured include the aerodynamic effects due to changes in the total-pressure-loss characteristics of the intake and exhaust openings of the air-exchange system, total-pressure distributions in the flow field at locations around the wind tunnel circuit, the locations of the maximum total-pressure contours, and the aerodynamic changes caused by the installation of the acoustic barrier in the southwest corner of the wind tunnel. The model tests reveal the changes in the aerodynamic performance of the 1986 version of the 40- by 80-Foot Wind Tunnel compared with the performance of the 1982 configuration