It is a long standing open problem to find an explicit description of the stable set polytope of clawfree graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even no conjecture at hand today. Such a conjecture exists for the class of quasi-line graphs. This class of graphs is a proper superclass of line g...

We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an assumption that the terminal alphabet is fixed, the membership problem for regular grammars (given v in binary and a regular commutative grammar G, does G generate v...

Let Σ = X ∪ X = {x1, x2, ..., xm, x −1 1 , x 2 , ..., x m } and let G be a group with set of generators Σ. Let L(G) = {ω ∈ Σ∗ | ω ≡ e (mod G)} ⊆ Σ∗ be the group language representing G, where Σ∗ is a free monoid over Σ and e is the identity in G. The problem of determining whether a context-free language is subset of a group language is discussed. Polynomial algorithms are presented for testing...

Straight-line programs (SLPs) offer powerful text compression by representing a text T [1, u] in terms of a restricted context-free grammar of n rules, so that T can be recovered in O(u) time. However, the problem of operating the grammar in compressed form has not been studied much. We present a grammar representation whose size is of the same order of that of a plain SLP representation, and c...

We analyze a simple approximation scheme based on the Morita-approach for the example of the mean field random field Ising model where it is claimed to be exact in some of the physics literature. We show that the approximation scheme is flawed, but it provides a set of equations whose metastable solutions surprisingly yield the correct solution of the model. We explain how the same equations ap...

− By a reduction to Post’s Correspondence Problem we provide a direct proof of the known fact that the inclusion problem for unambiguous context-free grammars is undecidable. The argument or some straightforward modification also applies to some other subclasses of context-free languages such as linear languages, sequential languages, and DSClanguages (i.e., languages generated by context-free ...

— We prove: 1) for any linear language L, it is recursively unsolvable to détermine whether L is an 1RS language; 2) for any deterministic context-free language L, it is recursively solvable to détermine whether L is an 1RS language; 3) there exists an 1RS linear language containing the concaténation product oftwo infinité contextfree languages.

in this paper, chaotic motion analysis and its control for a non-planar non-linear cantilever beam with axial and lateral parametric excitation in the free end is accomplished. this is a new method for control of chaotic motion of a non-linear planar beam. in this survey, internal resonance of the beam is 2:1 and the initial resonance is in the outside of plane and it is assumed a sub-resonance...

Abstract: This study is carried out to describe the behaviour of vehicles flow on the road, in the presence of blocking effects. A non-linear three dimensional system of ordinary differential equations is used to describe vehicles flow on the road. The study classify total vehicles population on the road into three compartments as Free – Slow – Released vehicles. The formulated model is well-po...

Calculating total cast of bank resources procurement methods which include current -free loan deposit, saving interest-free loan deposit, regular and net short-term investment deposit, long-term investment deposit and surety bond cash deposit and presenting their optimal integration require precise scientific studies. Hence, this study is an attempt to know which methods are the best optimal in...