Related papers: A short note on Simulation and Abstraction
This Liber Amicorum is a collection of essays ranging from personal memories to technical contributions. It is a tribute to Dave Schmidt and his career, and was composed at the occasion of his sixtieth birthday.
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators.…
Abstraction is a commonly used process to represent some low-level system by a more coarse specification with the goal to omit unnecessary details while preserving important aspects. While recent work on abstraction in the situation…
Analytic concepts contribute to our understanding of randomness of reals via algorithmic tests. They also influence the interplay between randomness and lowness notions. We provide a survey, written on the occasion of Rod Downey's 60th…
This paper is concerned with a compositional approach for constructing abstractions of interconnected discrete-time stochastic control systems. The abstraction framework is based on new notions of so-called stochastic simulation functions,…
Abstraction is a fundamental tool for reasoning about complex systems. Program abstraction has been utilized to great effect for analyzing deterministic programs. At the heart of program abstraction is the relationship between a concrete…
With the increasing ubiquity of safety-critical autonomous systems operating in uncertain environments, there is a need for mathematical methods for formal verification of stochastic models. Towards formally verifying properties of…
At the intersection of dynamical systems, control theory, and formal methods lies the construction of symbolic abstractions: these typically represent simpler, finite-state models whose behavior mimics that of an underlying concrete system…
The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…
This is, with minor modifications, a text read at the 114th Statistical Mechanics meeting, in honor of D.Ruelle and Y.Sinai, at Rutgers, Dec.13-15, 2015. It does not attempt to analyze, or not even just quote, all works of David Ruelle; I…
Stabilizer simulation can efficiently simulate an important class of quantum circuits consisting exclusively of Clifford gates. However, all existing extensions of this simulation to arbitrary quantum circuits including non-Clifford gates…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
In this paper, we introduce a compositional method for the construction of finite abstractions of interconnected discrete-time switched systems. Particularly, we use a notion of so-called alternating simulation function as a relation…
This paper formulates and studies the concepts of approximate (alternating) bisimulation relations characterizing equivalence relations between interconnected systems and their abstractions. These equivalence relations guarantee that the…
Abstraction-based control design is a promising approach for ensuring safety-critical control of complex cyber-physical systems. A key aspect of this methodology is the relation between the original and abstract systems, which ensures that…
One important factor determining the computational complexity of evaluating a probabilistic network is the cardinality of the state spaces of the nodes. By varying the granularity of the state spaces, one can trade off accuracy in the…
Lecture Notes for the Erice Summer School 2005 Computer Simulations in Condensed Matter: from Materials to Chemical Biology. Perspectives in celebration of the 65th Birthday of Mike Klein organized by Kurt Binder, Giovanni Ciccotti and…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…