Even though quantum computation is useful for solving certain problems, classical computation is more powerful in some cases. Thus, it is significant to compare the abilities of quantum computation and its classical counterpart, based on such a simple computation model as automata. In this paper we focus on the quantum pushdown automata which were defined by Golovkins in 2000, who showed that the class of languages recognized by quantum pushdown automata properly contains the class of languages recognized by finite automata. However, no one knows the entire relationship between the recognitive abilities of quantum and classical pushdown automata. As a part, we show a proposition that quantum pushdown automata can deterministically solve a certain problem that cannot be solved by any deterministic pushdown automata.

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L ast month, Tokyo Medical University (TMU) announced Yukiko Hayashi as its first female president. This comes on the heels of discovering that the insitution had manipulated entrance exam scores for many years to curb female enrollment. Hayashi may be an attempt by TMU to restore its reputation, but the scandal should be a wake-up call for Japanese society to ensure that men and women have equal opportunities to succeed. TMU admitted to engaging in gender discrimination because affiliated hospitals wanted more male graduates. Apparently, the university believed that female physicians are more likely to leave the medical profession because they cannot cope with demanding hospital schedules. Whereas misconduct of this scale can make the headlines, more subtle barriers discourage women from attaining various roles in Japan. Lack of gender parity is particularly severe in the science, technology, engineering, and mathematics (STEM) and medical fields. For example, the Japanese female-to-male ratio of physicians is the lowest among member countries of the Organization for Economic Cooperation and Development (OECD), hovering around 21% compared with the OECD average of 47%. Yet, Japan boasts one of the most sophisticated educational systems in the world. Japanese 15-year-old students are among the highest performers in mathematics and science according to the OECD's Programme for International Student Assessment (PISA). However, a gender gap is noticeable, especially among top-tier students. The latest PISA assessment in 2015 indicates that Japanese boys outperform girls in mathematics by ~15% of a standard deviation on the achievement scale. Among the top 10% of students in Japan, there is an even larger gender gap in both mathematics and science. But by international standards, Japanese girls perform at very high levels. For example, the highest-achieving girls in Japan performed significantly above the highest-achieving boys from most of the other 70 education systems assessed by PISA in both mathematics and science.