Treatment of Epsilon-Moves in Subset Construction

The paper discusses the problem of determinising finite-state automata containing large numbers of epsilon-moves. Experiments with finite-state approximations of natural language grammars often give rise to very large automata with a very large number of epsilon-moves. The paper identifies three subset construction algorithms which treat epsilon-moves. A number of experiments has been performed which indicate that the algorithms differ considerably in practice. Furthermore, the experiments suggest that the average number of epsilon-moves per state can be used to predict which algorithm is likely to perform best for a given input automaton

Mutations that Separate the Functions of the Proofreading Subunit of the Escherichia coli Replicase

The dnaQ gene of Escherichia coli encodes the Ɛ subunit of DNA polymerase III, which provides the 3\u27 - 5\u27 exonuclease proofreading activity of the replicative polymerase. Prior studies have shown that loss of Ɛ leads to high mutation frequency, partially constitutive SOS, and poor growth. In addition, a previous study from our laboratory identified dnaQ knockout mutants in a screen for mutants specifically defective in the SOS response after quinolone (nalidixic acid) treatment. To explain these results, we propose a model whereby, in addition to proofreading, Ɛ plays a distinct role in replisome disassembly and/or processing of stalled replication forks. To explore this model, we generated a pentapeptide insertion mutant library of the dnaQgene, along with site-directed mutants, and screened for separation of function mutants. We report the identification of separation of function mutants from this screen, showing that proofreading function can be uncoupled from SOS phenotypes (partially constitutive SOS and the nalidixic acid SOS defect). Surprisingly, the two SOS phenotypes also appear to be separable from each other. These findings support the hypothesis that Ɛ has additional roles aside from proofreading. Identification of these mutants, especially those with normal proofreading but SOS phenotype(s), also facilitates the study of the role of e in SOS processes without the confounding results of high mutator activity associated with dnaQ knockout mutants

Order-Invariant MSO is Stronger than Counting MSO in the Finite

We compare the expressiveness of two extensions of monadic second-order logic (MSO) over the class of finite structures. The first, counting monadic second-order logic (CMSO), extends MSO with first-order modulo-counting quantifiers, allowing the expression of queries like ``the number of elements in the structure is even''. The second extension allows the use of an additional binary predicate, not contained in the signature of the queried structure, that must be interpreted as an arbitrary linear order on its universe, obtaining order-invariant MSO. While it is straightforward that every CMSO formula can be translated into an equivalent order-invariant MSO formula, the converse had not yet been settled. Courcelle showed that for restricted classes of structures both order-invariant MSO and CMSO are equally expressive, but conjectured that, in general, order-invariant MSO is stronger than CMSO. We affirm this conjecture by presenting a class of structures that is order-invariantly definable in MSO but not definable in CMSO.Comment: Revised version contributed to STACS 200

Differential calculi on finite groups

A brief review of bicovariant differential calculi on finite groups is given, with some new developments on diffeomorphisms and integration. We illustrate the general theory with the example of the nonabelian finite group S_3.Comment: LaTeX, 16 pages, 1 figur

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Gravity on Finite Groups

Gravity theories are constructed on finite groups G. A self-consistent review of the differential calculi on finite G is given, with some new developments. The example of a bicovariant differential calculus on the nonabelian finite group S_3 is treated in detail, and used to build a gravity-like field theory on S_3.Comment: LaTeX, 26 pages, 1 figure. Corrected misprints and formula giving exterior product of n 1-forms. Added note on topological actio

Pushdown Automata Correspond to Context Free Grammars

One of the standard proofs about pushdown automata and context free grammars is that both correspond to the context free languages. The proof is typically in two parts, one showing that for every context free grammar there is a corresponding pushdown automaton, and the other showing that for every pushdown automaton there is a corresponding context free grammar. This resource provides the latter proof for Maheshwari and Smid\u27s pushdown automata