Evaluating Matrix Circuits

The circuit evaluation problem (also known as the compressed word problem) for finitely generated linear groups is studied. The best upper bound for this problem is $\mathsf{coRP}$, which is shown by a reduction to polynomial identity testing. Conversely, the compressed word problem for the linear group $\mathsf{SL}_3(\mathbb{Z})$ is equivalent to polynomial identity testing. In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in $\mathsf{DET} \subseteq \mathsf{NC}^2$. Within the larger class of polycyclic groups we find examples where the compressed word problem is at least as hard as polynomial identity testing for skew arithmetic circuits

Tree Compression with Top Trees Revisited

We revisit tree compression with top trees (Bille et al, ICALP'13) and present several improvements to the compressor and its analysis. By significantly reducing the amount of information stored and guiding the compression step using a RePair-inspired heuristic, we obtain a fast compressor achieving good compression ratios, addressing an open problem posed by Bille et al. We show how, with relatively small overhead, the compressed file can be converted into an in-memory representation that supports basic navigation operations in worst-case logarithmic time without decompression. We also show a much improved worst-case bound on the size of the output of top-tree compression (answering an open question posed in a talk on this algorithm by Weimann in 2012).Comment: SEA 201

Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)

In this paper, a compressed membership problem for finite automata, both deterministic and non-deterministic, with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are recompressed, so that substrings of the input text are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, such recompression induces only small changes in the automaton, in particular, the size of the automaton remains polynomial. Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter and extending the partial result of Lohrey and Mathissen; as it is already known, that this problem is NP-hard, we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P; for this problem, only trivial upper-bound PSPACE was known

Unary Pushdown Automata and Straight-Line Programs

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards

A really simple approximation of smallest grammar

In this paper we present a really simple linear-time algorithm constructing a context-free grammar of size O(g log (N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this string. The algorithm works for arbitrary size alphabets, but the running time is linear assuming that the alphabet Sigma of the input string can be identified with numbers from 1,ldots, N^c for some constant c. Algorithms with such an approximation guarantee and running time are known, however all of them were non-trivial and their analyses were involved. The here presented algorithm computes the LZ77 factorisation and transforms it in phases to a grammar. In each phase it maintains an LZ77-like factorisation of the word with at most l factors as well as additional O(l) letters, where l was the size of the original LZ77 factorisation. In one phase in a greedy way (by a left-to-right sweep and a help of the factorisation) we choose a set of pairs of consecutive letters to be replaced with new symbols, i.e. nonterminals of the constructed grammar. We choose at least 2/3 of the letters in the word and there are O(l) many different pairs among them. Hence there are O(log N) phases, each of them introduces O(l) nonterminals to a grammar. A more precise analysis yields a bound O(l log(N/l)). As l \leq g, this yields the desired bound O(g log(N/g)).Comment: Accepted for CPM 201

An Integrated Object Model and Method Framework for Subject-Centric e-Research Applications

A framework that integrates an object model, research methods (workflows), the capture of experimental data sets and the provenance of those data sets for subject-centric research is presented. The design of the Framework object model draws on and extends pre-existing object models in the public domain. In particular the Framework tracks the state and life cycle of a subject during an experimental method, provides for reusable subjects, primary, derived and recursive data sets of arbitrary content types, and defines a user-friendly and practical scheme for citably identifying information in a distributed environment. The Framework is currently used to manage neuroscience Magnetic Resonance and microscopy imaging data sets in both clinical and basic neuroscience research environments. The Framework facilitates multi-disciplinary and collaborative subject-based research, and extends earlier object models used in the research imaging domain. Whilst the Framework has been explicitly validated for neuroimaging research applications, it has broader application to other fields of subject-centric research

Point-Counterpoint: Should Attendance Be Required In Collegiate Classrooms?

This paper examines two divergent viewpoints about whether or not class attendance should be mandatory in higher education. The authors, both accounting professors at the same institution, delineate their respective viewpoints citing school policy, federal regulations and academic freedom as factors which motivate their attendance policy

Faculty Perceptions Of Attendance Policy In An AACSB School

The issue of attendance policies has been studied by higher education professionals for nearly a century. Prior research has shown a strong statistical link between class attendance and student grades. The aim of our research project is to gauge the attitudes and policies of business school professors in an AACSB accredited school on this topic. An online survey was conducted during the early Fall 2018 semester. Results suggest the vast majority of respondents institute an attendance policy in their classes. Respondents taught courses at both the graduate and undergraduate levels and are a diverse set of faculty as indicated by academic rank, age, gender and level of education

Processing Succinct Matrices and Vectors

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of a semiring (instead of 0 and 1). A simple example shows that the product of two MTDD-represented matrices cannot be represented by an MTDD of polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by allowing componentwise symbolic addition of variables (of the same dimension) in rules. It is shown that accessing an entry, equality checking, matrix multiplication, and other basic matrix operations can be solved in polynomial time for MTDD_+-represented matrices. On the other hand, testing whether the determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of CSR 201

Deciding Equivalence of Linear Tree-to-Word Transducers in Polynomial Time

We show that the equivalence of deterministic linear top-down tree-to-word transducers is decidable in polynomial time. Linear tree-to-word transducers are non-copying but not necessarily order-preserving and can be used to express XML and other document transformations. The result is based on a partial normal form that provides a basic characterization of the languages produced by linear tree-to-word transducers.Comment: short version of this paper will be published in the proceedings of the 20th Conference on Developments in Language Theory (DLT 2016), Montreal, Canad