39 research outputs found
Linear iterated pushdowns
This paper discusses variants of nondeterministic one-way S-automata and context-free S-grammars where S is a storage type. The framework that these systems provide can be used to give alternative formulations of embedded pushdown automata and linear indexed grammars. The embedded pushdown automata is obtained by means of a linear version of a class of storage types called iterated pushdowns. Linear indexed grammar is obtained by using the pushdown storage type and restricting the way in which the grammar uses its storage
A hierarchy of mildly context sensitive dependency grammar
The paper presents Colored Multiplanar Link Grammars (CMLG). These grammars are reducible to extended right-linear S-grammars (Wartena 2001) where the storage type S is a concatenation of c pushdowns. The number of colors available in these grammars induces a hierarchy of Classes of CMLGs. By fixing also another parameter in CMLGs, namely the bound t for non-projectivity depth, we get c-Colored t-Non-projective Dependency Grammars (CNDG) that generate acyclic dependency graphs. Thus, CNDGs form a two-dimensional hier- archy of dependency grammars. A part of this hierarchy is mildly context-sensitive and non-projective.The paper presents Colored Multiplanar Link Grammars (CMLG). These grammars are reducible to extended right-linear S-grammars (Wartena 2001) where the storage type S is a concatenation of c pushdowns. The number of colors available in these grammars induces a hierarchy of Classes of CMLGs. By fixing also another parameter in CMLGs, namely the bound t for non-projectivity depth, we get c-Colored t-Non-projective Dependency Grammars (CNDG) that generate acyclic dependency graphs. Thus, CNDGs form a two-dimensional hier- archy of dependency grammars. A part of this hierarchy is mildly context-sensitive and non-projective.Peer reviewe
Traces and Characteristic Classes in Infinite Dimensions
This paper surveys topological results obtained from characteristic classes
built from the two types of traces on the algebra of pseudodifferential
operators of nonpositive order. The main results are the construction of a
universal -polynomial and Chern character that control the -index
theorem for all circle actions on a fixed vector bundle over a manifold, and
, for the diffeomorphism
group of circle bundles with large first Chern class over projective
algebraic Kaehler surfaces.Comment: Parts of Section 2.3 are not correct. This is discussed in T.
McCauley, "S^1-Equivariant Chern-Weil Constructions on Loop Spaces,"
arXiv:1507.0862
Where do the tedious products of zetas come from?
Lamentably, the full analytical content of the epsilon-expansion of the
master two-loop two-point function, with arbitrary self-energy insertions in
4-2epsilon dimensions, is still unknown. Here we show that multiple zeta values
(MZVs) of weights up to 12 suffice through O(epsilon^9). Products of primitive
MZVs are generated by a processes of "pseudo-exponentiation"" whose
combinatorics faithfully accord with expectations based on Kreimer's modified
shuffle product and on the Drinfeld-Deligne conjecture. The existence of such a
mechanism, relating thousands of complicated rational numbers, enables us to
identify precise and simple combinations of MZVs specific to quantum field
theories in even numbers of spacetime dimensions.Comment: 5 pages, LaTeX, uses npb.sty, talk given at "RadCor 2002 - Loops and
Legs 2002", Kloster Banz, Germany, Sep 8-13, 200
Synchronous Subsequentiality and Approximations to Undecidable Problems
We introduce the class of synchronous subsequential relations, a subclass of
the synchronous relations which embodies some properties of subsequential
relations. If we take relations of this class as forming the possible
transitions of an infinite automaton, then most decision problems (apart from
membership) still remain undecidable (as they are for synchronous and
subsequential rational relations), but on the positive side, they can be
approximated in a meaningful way we make precise in this paper. This might make
the class useful for some applications, and might serve to establish an
intermediate position in the trade-off between issues of expressivity and
(un)decidability.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Extended macro grammars and stack controlled machines
K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semi-AFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type D, the stack controlled machine type corresponding to D is introduced, denoted S(D), and the checking-stack controlled machine type CS(D). The data structure of this machine is a stack which controls a pushdown of data structures from D. If D accepts K, then S(D) accepts B(K) and CS(D) accepts LB(K). Thus the classes B(K) are characterized by stack controlled machines and the classes LB(K), i.e., the full hyper-AFLs, by checking-stack controlled machines. A full basic-AFL is a full AFL K such that B(K)C K. Every full basic-AFL is a full hyper-AFL, but not vice versa. The class of OI macro languages (i.e., indexed languages, i.e., nested stack automaton languages) is a full basic-AFL, properly containing the smallest full basic-AFL. The latter is generated by the ultrabasic macro grammars and accepted by the nested stack automata with bounded depth of nesting (and properly contains the stack languages, the ETOL languages, i.e., the smallest full hyper-AFL, and the basic macro languages). The full basic-AFLs are characterized by bounded nested stack controlled machines