We consider recognizable languages of cospans in adhesive categories, of which recognizable graph languages are a special case. We show that such languages are closed under concatenation, i.e. under cospan composition, by providing a concrete construction that creates a concatenation automaton from two given automata. The construction is considerably more complex than the corresponding construc...

The parallel and serial concatenation of codes is well established as a practical means of achieving excellent performance. In this paper, we introduce the parallel and serial concatenation of single parity check (SPC) product codes. The weight distribution of these codes is analyzed and the performance is bounded. Simulation results confirm these bounds at high signal-to-noise ratios. The perf...

Abstract We introduce the concept of TRAP (Traces and Permutations), which can roughly be viewed as a wheeled PROP (Products Permutations) without unit. TRAPs are equipped with horizontal concatenation partial trace maps. Continuous morphisms on an infinite-dimensional topological space smooth kernels (respectively, smoothing operators) closed manifold form but not PROP. build free objects in c...

i. Union, intersection, set concatenation, Kleene-star, set subtraction, complement Answer: Union: S ∪ T = { x | x ∈ S or x ∈ T} Intersection: S ∩ T = { x | x ∈ S and x ∈ T} Concatenation: S ◦ T = { xy | x ∈ S, y ∈ T} Kleene-star: S = { w1w2 · · ·wk | k ≥ 0, wi ∈ S ∀ i = 1, 2, . . . , k} Subtraction: S − T = { x | x ∈ S, x 6∈ T} Complement: S = { x ∈ Ω | x 6∈ S} = Ω− S, where Ω is the universe ...

We deene an extension of a second-order type system with records, subtyping and record concatenation. This system can model the most important concepts of object-oriented languages. The novelty in our approach is that concatenation is only permitted if the types on common elds agree. We give examples of how object-oriented concepts can be modeled and show how the system can be translated to a t...