相关论文: A Formalization of the Process Algebra CCS in HOL4

This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…

We present an algorithm for converting proofs from the OpenTheory interchange format, which can be translated to and from any of the HOL family of proof languages (HOL4, HOL Light, ProofPower, and Isabelle), into the ZFC-based Metamath…

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…

We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying…

Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…

General frameworks have been recently proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools.…

Building on the standard theory of process algebra with priorities, we identify a new scheduling mechanism, called "constructive reduction" which is designed to capture the essence of synchronous programming. The distinctive property of…

Cause-consequence Diagram (CCD) is widely used as a deductive safety analysis technique for decision-making at the critical-system design stage. This approach models the causes of subsystem failures in a highly-critical system and their…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a semantical platform and research program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth which it has more…

Coherent state operators (CSO) are defined as operator valued functions on G=SL(n,C), homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional…

An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a…

The term `Convected Scheme' (CS) refers to a family of algorithms, most usually applied to the solution of Boltzmann's equation, which uses a method of characteristics in an integral form to project an initial cell forward to a group of…

The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…

Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and…

Pauli first noticed the hidden SO(4) symmetry for the Hydrogen atom in the early stages of quantum mechanics [1]. Departing from that symmetry, one can recover the spectrum of a spinless hydrogen atom and the degeneracy of its states…

In our previous work [1] we described quantized computation using Horn clauses and based the semantics, dubbed as entanglement semantics as a generalization of denotational and distribution semantics, and founded it on quantum probability…

Self-evolving scientific agents capable of conquering the hard tail of formal mathematics require Compositional Learning Behaviours (CLBs) -- the capacity to ground and recombine novel symbolic structures in context, beyond mere…

Formal modeling of cyber-physical systems (CPS) is hard, because they pose the double challenge of combined discrete-continuous dynamics and concurrent behavior. Existing formal specification and verification languages for CPS are designed…

The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and…

Concurrent separation logic (CSL) is a specification logic for concurrent imperative programs with shared memory and locks. In this paper, we develop a concurrent and interactive account of the logic inspired by asynchronous game semantics.…