Logic Meets Algebra: the Case of Regular Languages

The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical formalism required to define them. The algebraic point of view on automata is an essential complement of this classification: by providing alternative, algebraic characterizations for the classes, it often yields the only opportunity for the design of algorithms that decide expressibility in some logical fragment. We survey the existing results relating the expressibility of regular languages in logical fragments of MSO[S] with algebraic properties of their minimal automata. In particular, we show that many of the best known results in this area share the same underlying mechanics and rely on a very strong relation between logical substitutions and block-products of pseudovarieties of monoid. We also explain the impact of these connections on circuit complexity theory.Comment: 37 page

Garside combinatorics for Thompson's monoid F+F^+ and a hybrid with the braid monoid B_∞+B\_\infty^+

On the model of simple braids, defined to be the left divisors of Garside's elements $\Delta\_n$ in the monoid $B\_\infty^+$ , we investigate simple elements in Thompson's monoid $F^+$ and in a larger monoid $H^+$ that is a hybrid of $B\_\infty^+$ and $F^+$ : in both cases, we count how many simple elements left divide the right lcm of the first n -- 1 atoms, and characterize their normal forms in terms of forbidden factors. In the case of $H^+$, a generalized Pascal triangle appears

Cell cycle specific radiosensitisation by the disulfiram and copper complex

The disulfiram and copper complex (DSF:Cu) has emerged as a potent radiosensitising anti-cancer agent. The ability of copper to stabilise DSF in a planar conformation and to inhibit DNA replication enzymes stimulated our investigation of the effect of DSF:Cu on cell cycle regulation. Flow cytometry and immunoblotting were used to assess the effect of DSF:Cu on cell cycle progression of the neuroblastoma cell line SK-N-BE(2c) and the glioma cell line UVW. Treatment with 0.1 and 0.3 μM DSF:Cu inhibited DNA synthesis in SK-N-BE(2c) and UVW cells, respectively. The increased potency of ionising radiation treatment induced by DSF:Cu and/or gemcitabine was determined by clonogenic assay. Treatment with 0.3 μM DSF:Cu resulted in greater radiation kill, exemplified by dose enhancement factor values of 2.64 and 2.84 in SKN-BE(2c) and UVW cells, respectively. Although DSF:Cu failed to sensitise S phase cells to irradiation, we observed that DSF:Cu radiosensitisation was potentiated by the S phase-specific cytotoxic drug gemcitabine. The efficacy of the combination treatment consisting of DSF:Cu, gemcitabine and ionising radiation was scheduledependent. Together, these results describe cell cycle specific radiosensitisation by DSF:Cu. The well-established toxicity profiles of DSF and gemcitabine should facilitate their evaluation as a combination treatment in patients undergoing radiotherapy

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