17,280 research outputs found

### Virasoro Symmetries of the Extended Toda Hierarchy

We prove that the extended Toda hierarchy of \cite{CDZ} admits nonabelian Lie
algebra of infinitesimal symmetries isomorphic to the half of the Virasoro
algebra. The generators $L_m$, $m\geq -1$ of the Lie algebra act by linear
differential operators onto the tau function of the hierarchy. We also prove
that the tau function of a generic solution to the extended Toda hierarchy is
annihilated by a combination of the Virasoro operators and the flows of the
hierarchy. As an application we show that the validity of the Virasoro
constraints for the $CP^1$ Gromov-Witten invariants and their descendents
implies that their generating function is the logarithm of a particular tau
function of the extended Toda hierarchy.Comment: A remark at the end of Section 5 is added; more detailed explanations
in Appendix; references adde

### The generalized no-ghost theorem for N=2 SUSY critical strings

We prove the no-ghost theorem for the N=2 SUSY strings in (2,2) dimensional
flat Minkowski space. We propose a generalization of this theorem for an
arbitrary geometry of the N=2 SUSY string theory taking advantage of the N=4
SCA generators present in this model. Physical states are found to be the
highest weight states of the N=4 SCA.Comment: 13

### A New Description of the E_6 Singularity

We discuss a new type of Landau-Ginzburg potential for the E_6 singularity of
the form $W=const+(Q_1(x)+P_1(x)\sqrt{P_2(x)})/x^3$ which featured in a recent
study of heterotic/typeII string duality. Here $Q_1,P_1$ and $P_2$ are
polynomials of degree 15,10 and 10, respectively. We study the properties of
the potential in detail and show that it gives a new and consistent description
of the E_6 singularity.Comment: LaTeX, 13 pages, no figure

### Complexity Analysis of Precedence Terminating Infinite Graph Rewrite Systems

The general form of safe recursion (or ramified recurrence) can be expressed
by an infinite graph rewrite system including unfolding graph rewrite rules
introduced by Dal Lago, Martini and Zorzi, in which the size of every normal
form by innermost rewriting is polynomially bounded. Every unfolding graph
rewrite rule is precedence terminating in the sense of Middeldorp, Ohsaki and
Zantema. Although precedence terminating infinite rewrite systems cover all the
primitive recursive functions, in this paper we consider graph rewrite systems
precedence terminating with argument separation, which form a subclass of
precedence terminating graph rewrite systems. We show that for any precedence
terminating infinite graph rewrite system G with a specific argument
separation, both the runtime complexity of G and the size of every normal form
in G can be polynomially bounded. As a corollary, we obtain an alternative
proof of the original result by Dal Lago et al.Comment: In Proceedings TERMGRAPH 2014, arXiv:1505.06818. arXiv admin note:
text overlap with arXiv:1404.619

### Formalizing Termination Proofs under Polynomial Quasi-interpretations

Usual termination proofs for a functional program require to check all the
possible reduction paths. Due to an exponential gap between the height and size
of such the reduction tree, no naive formalization of termination proofs yields
a connection to the polynomial complexity of the given program. We solve this
problem employing the notion of minimal function graph, a set of pairs of a
term and its normal form, which is defined as the least fixed point of a
monotone operator. We show that termination proofs for programs reducing under
lexicographic path orders (LPOs for short) and polynomially quasi-interpretable
can be optimally performed in a weak fragment of Peano arithmetic. This yields
an alternative proof of the fact that every function computed by an
LPO-terminating, polynomially quasi-interpretable program is computable in
polynomial space. The formalization is indeed optimal since every
polynomial-space computable function can be computed by such a program. The
crucial observation is that inductive definitions of minimal function graphs
under LPO-terminating programs can be approximated with transfinite induction
along LPOs.Comment: In Proceedings FICS 2015, arXiv:1509.0282

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