The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

We define the problem “identity check”: Given a classical description of a quantum circuit, determine whether it is almost equivalent to the identity. Explicitly, the task is to decide whether the corresponding unitary is close to a complex multiple of the identity matrix with respect to the operator norm. We show that this problem is QMA-complete. A generalization of this problem is “equivalen...

This study investigated the roles of problem structure and strategy use in problem encoding. Fourthgrade students solved and explained a set of typical addition problems (e.g., 5 + 4 + 9 + 5 = ) and mathematical equivalence problems (e.g., 4 + 3 + 6 = 4 + or 6 + 4 + 5 = + 5). Next, they completed an encoding task in which they reconstructed addition and equivalence problems after viewing each f...

Deciding equivalence of probabilistic automata is a key problem for establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test based on polynomial identity testing outperformed deterministic algorithms. In this paper we show that polynomial identity testing yields efficient algorithms for various generalisations of the...

The supervisory control of discrete event systems provides a framework for control of eventdriven systems. Applications of supervisory control theory include protocol design for communication processes, control logic synthesis in manufacturing systems, and collision avoidance in human-computer interaction systems. When designing a system at a certain level of abstraction, lower level details of...

Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, i.e. any categorical interpretation of the logic compatible with its cut-elimination procedure. This notion can usually be captured syntactically by a set of rule permutations. Very generally, proofnets can be define...

In this paper, we present a much simpler, direct and elegant approach to the equivalence problem of measure many one-way quantum finite automata (MM1QFAs). The approach is essentially generalized from the work of Carlyle [J. Math. Anal. Appl. 7 (1963) 167-175]. Namely, we reduce the equivalence problem of MM-1QFAs to that of two (initial) vectors. As an application of the approach, we utilize i...

We study the computational difficulty of deciding whether two matrices generate equivalent linear codes, i.e., codes that consist of the same codewords up to a fixed permutation on the codeword coordinates. We call this problem Code Equivalence. Using techniques from the area of interactive proofs, we show on the one hand, that under the assumption that the polynomial-time hierarchy does not co...