Formal mechanization of device interactions with a process algebra

The principle emphasis is to develop a methodology to formally verify correct synchronization communication of devices in a composed hardware system. Previous system integration efforts have focused on vertical integration of one layer on top of another. This task examines 'horizontal' integration of peer devices. To formally reason about communication, we mechanize a process algebra in the Higher Order Logic (HOL) theorem proving system. Using this formalization we show how four types of device interactions can be represented and verified to behave as specified. The report also describes the specification of a system consisting of an AVM-1 microprocessor and a memory management unit which were verified in previous work. A proof of correct communication is presented, and the extensions to the system specification to add a direct memory device are discussed

Towards composition of verified hardware devices

Computers are being used where no affordable level of testing is adequate. Safety and life critical systems must find a replacement for exhaustive testing to guarantee their correctness. Through a mathematical proof, hardware verification research has focused on device verification and has largely ignored system composition verification. To address these deficiencies, we examine how the current hardware verification methodology can be extended to verify complete systems

Searching for a Solution to Program Verification=Equation Solving in CCS

International audienceUnder non-exponential discounting, we develop a dynamic theory for stopping problems in continuous time. Our framework covers discount functions that induce decreasing impatience. Due to the inherent time inconsistency, we look for equilibrium stopping policies, formulated as fixed points of an operator. Under appropriate conditions, fixed-point iterations converge to equilibrium stopping policies. This iterative approach corresponds to the hierarchy of strategic reasoning in game theory and provides “agent-specific” results: it assigns one specific equilibrium stopping policy to each agent according to her initial behavior. In particular, it leads to a precise mathematical connection between the naive behavior and the sophisticated one. Our theory is illustrated in a real options model

Unique Solutions of Contractions, CCS, and their HOL Formalisation

The unique solution of contractions is a proof technique for bisimilarity that overcomes certain syntactic constraints of Milner's "unique solution of equations" technique. The paper presents an overview of a rather comprehensive formalisation of the core of the theory of CCS in the HOL theorem prover (HOL4), with a focus towards the theory of unique solutions of contractions. (The formalisation consists of about 20,000 lines of proof scripts in Standard ML.) Some refinements of the theory itself are obtained. In particular we remove the constraints on summation, which must be weakly-guarded, by moving to rooted contraction, that is, the coarsest precongruence contained in the contraction preorder.Comment: In Proceedings EXPRESS/SOS 2018, arXiv:1808.0807

Universal corner entanglement from twist operators

The entanglement entropy in three-dimensional conformal field theories (CFTs) receives a logarithmic contribution characterized by a regulator-independent function $a(\theta)$ when the entangling surface contains a sharp corner with opening angle $\theta$. In the limit of a smooth surface ($\theta\rightarrow\pi$), this corner contribution vanishes as $a(\theta)=\sigma\,(\theta-\pi)^2$. In arXiv:1505.04804, we provided evidence for the conjecture that for any $d=3$ CFT, this corner coefficient $\sigma$ is determined by $C_T$, the coefficient appearing in the two-point function of the stress tensor. Here, we argue that this is a particular instance of a much more general relation connecting the analogous corner coefficient $\sigma_n$ appearing in the $n$th R\'enyi entropy and the scaling dimension $h_n$ of the corresponding twist operator. In particular, we find the simple relation $h_n/\sigma_n=(n-1)\pi$. We show how it reduces to our previous result as $n\rightarrow 1$, and explicitly check its validity for free scalars and fermions. With this new relation, we show that as $n\rightarrow 0$, $\sigma_n$ yields the coefficient of the thermal entropy, $c_S$. We also reveal a surprising duality relating the corner coefficients of the scalar and the fermion. Further, we use our result to predict $\sigma_n$ for holographic CFTs dual to four-dimensional Einstein gravity. Our findings generalize to other dimensions, and we emphasize the connection to the interval R\'enyi entropies of $d=2$ CFTs.Comment: 26 + 15 pages, 6 + 1 figures, 4 + 1 tables; v2: minor modifications to match published version, references adde

A formalization of unique solutions of equations in process algebra

In this thesis, a comprehensive formalization of Milner's Calculus of Communicating Systems (also known as CCS) has been done in HOL theorem prover (HOL4), based on an old work in HOL88. This includes all classical properties of strong/weak bisimulation equivalences and observation congruence, a theory of congruence for CCS, various versions of ``bisimulation up to'' techniques, and several deep theorems, namely the ``coarsest congruence contained in weak equivalence'', and three versions of the ``unique solution of equations'' theorem in Milner's book. This work is further extended to support recent developments in Concurrency Theory, namely the ``contraction'' relation and the related ``unique solutions of contractions'' theorem found by Prof. Davide Sangiorgi, University of Bologna. As a result, a rather complete theory of ``contraction'' (and a similar relation called ``expansion'') for CCS is also formalized in this thesis. Further more, a new variant of contraction called ``observational contraction'' was found by the author during this work, based on existing contraction relation. It's formally proved that, this new relation is preserved by direct sums of CCS processes, and has a more elegant form of the ``unique solutions of contractions'' theorem without any restriction on the CCS grammar. The contribution of this thesis project is at least threefold: First, it can be seen as a formal verification of the core results in Prof.\ Sangiorgi's paper, and it provides all details for the informal proof sketches given in the paper. Second, a large piece of old proof scripts from the time of Hol88 (1990s) has been ported to HOL4 and made available to all its users. Third, it's a proof engineering research by itself on the correct formalization of process algebra, because the work has made extensive uses of some new features (e.g. coinductive relation) provided in recent versions of HOL4 (Kananaskis-11 and later)