Polynomial Loops: Beyond Termination

In the last years, several works were concerned with identifying classes of programswhere termination is decidable. We consider triangular weakly non-linear loops(twn-loops) over a ring Z ≤ S ≤ R_A , where R_A is the set of all real algebraicnumbers. Essentially, the body of such a loop is a single assignment(x_1, ..., x_d) ← (c_1 · x_1 + pol_1, ..., c_d · x_d + pol_d)where each x_i is a variable, c_i ∈ S, and each pol_i is a (possibly non-linear)polynomial over S and the variables x_{i+1}, ..., x_d. Recently, we showed thattermination of such loops is decidable for S = R_A and non-termination issemi-decidable for S = Z and S = Q.In this paper, we show that the halting problem is decidable for twn-loops over anyring Z ≤ S ≤ R_A. In contrast to the termination problem, where termination on allinputs is considered, the halting problem is concerned with termination on a giveninput. This allows us to compute witnesses for non-termination.Moreover, we present the first computability results on the runtime complexity ofsuch loops. More precisely, we show that for twn-loops over Z one can alwayscompute a polynomial f such that the length of all terminating runs is boundedby f( || (x_1, ..., x_d) || ), where || · || denotes the 1-norm. As a corollary, weobtain that the runtime of a terminating triangular linear loop over Z isat most linear.

Have a Look Around: The Effect of a ‘Push’ Activity on Future SAS Use

Although mandatory regular use of self-access centres is surprisingly common, this goes against the purpose of them to foster autonomous learning. However, some students never consider using such resources without being pushed to do so. In order to create an opportunity to discover a self-access station (SAS) at one Japanese university, a single assignment was designed and implemented requiring students to visit the SAS in order to answer questions related to its use and facilities. Thereafter, an end-of-term questionnaire was conducted to investigate how the assignment affected student awareness and use of the SAS, and whether they would have visited the SAS had there been no task. The results show that awareness of the SAS was raised. However, most students did not use the SAS post-assignment and indicated they would not have used it without the assignment. Reasons provided suggest time constraints, location, and issues of comfort to be contributing factors.

How Much!? Determining the Cost of an Assignment in an Organic Chemistry Class

Students in Organic Chemistry for Majors were required to write a paper as the culminating course assignment. Prior to completing this assignment, students could attend a library instruction session covering relevant databases and resources. Upon submission of their papers, bibliographies from 53 students were collected. Calculations were made to attempt a holistic account of costs associated with completing the assignment. Factors such as the cost of journals, databases, and librarian time were all included in the overall cost estimate, totalling $7,189.22 for this single assignment.