Parikh theorem was originally stated and proved by Rohkit Parikh in MIT research report in 1961. Many different proofs of this classical theorems were produced then; our goal is to give another proof using Chomsky-Schutzenberger representation theorem. We present the proof which doesn't use any formal language theory tool at all except the representation theorem, just some linear algebra.

This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation...

Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a datatypegeneric representation theorem. More precisely, we prove a representation theorem for a wide class of second-order functionals which are polymorphic over a class of functors. Types polymorphic over a class o...

The exact solution of the interacting many-body system is important and difficult to solve. In this paper, we introduce a group method solve problem using relation between permutation unitary group. We prove theorem first, then theorem, represent Hamiltonian by Casimir operators eigenvalues could give values energy thus those problems exactly. This maps onto an intermediate statistical represen...

There are two classes of nonlinear expectations, one is the Choquet expectation given by Choquet (1955), the other is the Peng’s g-expectation given by Peng (1997) via backward differential equations (BSDE). Recently, Peng raised the following question: can a g-expectation be represented by a Choquet expectation? In this paper, we provide a necessary and sufficient condition on g-expectations u...

We give a quadratic O(|X|) space representation based on a canonical tree for any subset family F ⊆ 2 closed under the union and the difference of its overlapping members. The cardinality of F is potentially in O(2), and the total cardinality of its members even higher. As far as we know this is the first representation result for such families. As an application of this framework we obtain a u...

This abstract is a summary of a lecture given at the Seminar of the Department of Logic and Methodology of Sciences, Wroc law University, 23 May 1985. The present work refers directly to the investigations of Buszkowski and Prucnal [1] and that of Esakia [2], generalizing their results. Our main representation theorem for co-diagonalizable algebras (Theorem 2) is obtained by application of cert...

We prove a representation theorem for Boolean contact algebras which implies that the axioms for the Region Connection Calculus [20] (RCC) are complete for the class of subalgebras of the algebras of regular closed sets of weakly regular connected T1 spaces.