arXiv subjects

Adnan Rashid

Publications and source records attributed to Adnan Rashid.

At least 19 recordsLinked to original sources

arXiv2026

ReasonOps: A Unified Operational Paradigm for Trustworthy Verified LLM Reasoning

Large Language Models (LLMs) have transformed artificial intelligence from primarily generative systems into increasingly capable reasoning agents. Recent advances in theorem proving, autoformalization, symbolic reasoning, and tool-augmented language models demonstrate substantial progress toward machine-assisted formal reasoning. However, current reasoning systems still suffer from hidden logical inconsistencies, hallucinated symbolic transitions, unsupported theorem applications, and limited reliability guarantees. Existing approaches remain fragmented across formal verification, runtime assurance, neuro-symbolic reasoning and trustworthy Artificial Intelligence (AI) research communities. This paper introduces ReasonOps, a unified operational paradigm for trustworthy verified reasoning systems. Inspired by operational ecosystems such as DevOps and MLOps, ReasonOps treats reasoning as a continuously monitored, verifiable, reliability-aware operational process rather than an isolated inference task. The proposed paradigm integrates semantic interpretation, autoformalization, symbolic reasoning, theorem proving, runtime assurance, probabilistic reliability estimation, and adaptive correction into a unified reasoning lifecycle. The paper further presents the ReasonOps architecture, demonstrates its workflow using an autonomous braking system analysis example, and discusses its potential role in future safety-critical autonomous AI systems. We argue that operational reasoning paradigms such as ReasonOps may become foundational infrastructure for next-generation trustworthy AI ecosystems.

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arXiv2026

On the Formalization of Network Topology Matrices in HOL

Network topology matrices are algebraic representations of graphs that are widely used in modeling and analysis of various applications including electrical circuits, communication networks and transportation systems. In this paper, we propose to use Higher-Order-Logic (HOL) based interactive theorem proving to formalize network topology matrices. In particular, we formalize adjacency, degree, Laplacian and incidence matrices in the Isabelle/HOL proof assistant. Our formalization is based on modelling systems as networks using the notion of directed graphs (unweighted and weighted), where nodes act as components of the system and weighted edges capture the interconnection between them. Then, we formally verify various classical properties of these matrices, such as indexing and degree. We also prove the relationships between these matrices in order to provide a comprehensive formal reasoning support for analyzing systems modeled using network topology matrices. To illustrate the effectiveness of the proposed approach, we formally analyze the Kron reduction of the Laplacian matrix and verify the total power dissipation in a generic resistive electrical network, both commonly used in power flow analysis.

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arXiv2024

Extending XReason: Formal Explanations for Adversarial Detection

Explainable Artificial Intelligence (XAI) plays an important role in improving the transparency and reliability of complex machine learning models, especially in critical domains such as cybersecurity. Despite the prevalence of heuristic interpretation methods such as SHAP and LIME, these techniques often lack formal guarantees and may produce inconsistent local explanations. To fulfill this need, few tools have emerged that use formal methods to provide formal explanations. Among these, XReason uses a SAT solver to generate formal instance-level explanation for XGBoost models. In this paper, we extend the XReason tool to support LightGBM models as well as class-level explanations. Additionally, we implement a mechanism to generate and detect adversarial examples in XReason. We evaluate the efficiency and accuracy of our approach on the CICIDS-2017 dataset, a widely used benchmark for detecting network attacks.

cs.AI↗

arXiv2024

Formalization of Biological Circuit Block Diagrams for formally analyzing Biomedical Control Systems in pHRI Applications

The control of Biomedical Systems in Physical Human-Robot Interaction (pHRI) plays a pivotal role in achieving the desired behavior by ensuring the intended transfer function and stability of subsystems within the overall system. Traditionally, the control aspects of biomedical systems have been analyzed using manual proofs and computer based analysis tools. However, these approaches provide inaccurate results due to human error in manual proofs and unverified algorithms and round-off errors in computer-based tools. We argue using Interactive reasoning, or frequently called theorem proving, to analyze control systems of biomedical engineering applications, specifically in the context of Physical Human-Robot Interaction (pHRI). Our methodology involves constructing mathematical models of the control components using Higher-order Logic (HOL) and analyzing them through deductive reasoning in the HOL Light theorem prover. We propose to model these control systems in terms of their block diagram representations, which in turn utilize the corresponding differential equations and their transfer function-based representation using the Laplace Transform (LT). These formally represented block diagrams are then analyzed through logical reasoning in the trusted environment of a theorem prover to ensure the correctness of the results. For illustration, we present a real-world case study by analyzing the control system of the ultrafilteration dialysis process.

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arXiv2024

Proof Recommendation System for the HOL4 Theorem Prover

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns from extensive libraries of HOL4 containing proofs of theorems. Consequently, it can accurately predict the next tactic(s) (proof step(s)) based on the history of previously employed tactics. The tool operates by reading a given sequence of tactics already used in a proof process (in our case, it contains at least three tactics), referred to as the current proof state, and provides recommendations for the next optimal proof step(s).

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arXiv2022

On the Formalization of the Heat Conduction Problem in HOL

Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the temperature distribution and diffusion of heat within a body. Due to the wider utility of these equations in various safety-critical applications, such as thermal protection systems, a formal analysis of the heat transfer is of utmost importance. In this paper, we propose to use higher-order-logic (HOL) theorem proving for formally analyzing the heat conduction problem in rectangular coordinates. In particular, we formally model the heat transfer as a one-dimensional heat equation for a rectangular slab using the multivariable calculus theories of the HOL Light theorem prover. This requires the formalization of the heat operator and formal verification of its various properties, such as linearity and scaling. Moreover, we use the separation of variables method for formally verifying the solution of the PDEs, which allows modeling the heat transfer in the slab under various initial and boundary conditions using HOL Light.

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arXiv2021

Towards the Formal Performance Analysis of Multistate Coherent Systems using HOL Theorem Proving

Many practical engineering systems and their components have multiple performance levels and failure modes. If these systems form a monotonically increasing structure function (system model) with respect to the performance of their components and also if all of their components affect the overall system performance, then they are said to be multistate coherent systems. Traditionally, the reliability analysis of these multistate coherent systems has been carried out using paper-and-pencil or simulation based methods. The former method is often prone to human errors, while the latter requires high computational resources for large and complex systems having components with multiple operational states. As a complimentary approach, we propose to use Higher-order-logic (HOL) theorem proving to develop a sound reasoning framework to analyze the reliability of multistate coherent systems in this paper. This framework allows us to formally verify generic mathematical properties about multistate coherent systems with an arbitrary number of components and their states. Particularly, we present the HOL formalization of series and parallel multistate coherent systems and formally verify their deterministic and probabilistic properties using the HOL4 theorem prover. For illustration purposes, we present the formal reliability analysis of the multistate oil and gas pipeline to demonstrate the effectiveness of our proposed framework.

cs.LO↗

arXiv2021

Formalization of Bond Graph using Higher-order-logic Theorem Proving

Bond graph is a unified graphical approach for describing the dynamics of complex engineering and physical systems and is widely adopted in a variety of domains, such as, electrical, mechanical, medical, thermal and fluid mechanics. Traditionally, these dynamics are analyzed using paper-and-pencil proof methods and computer-based techniques. However, both of these techniques suffer from their inherent limitations, such as human-error proneness, approximations of results and enormous computational requirements. Thus, these techniques cannot be trusted for performing the bond graph based dynamical analysis of systems from the safety-critical domains like robotics and medicine. Formal methods, in particular, higher-order-logic theorem proving, can overcome the shortcomings of these traditional methods and provide an accurate analysis of these systems. It has been widely used for analyzing the dynamics of engineering and physical systems. In this paper, we propose to use higher-order-logic theorem proving for performing the bond graph based analysis of the physical systems. In particular, we provide formalization of bond graph, which mainly includes functions that allow conversion of a bond graph to its corresponding mathematical model (state-space model) and the verification of its various properties, such as, stability. To illustrate the practical effectiveness of our proposed approach, we present the formal stability analysis of a prosthetic mechatronic hand using HOL Light theorem prover. Moreover, to help non-experts in HOL, we encode our formally verified stability theorems in MATLAB to perform the stability analysis of an anthropomorphic prosthetic mechatronic hand.

cs.LO↗

arXiv2021

Formalization of Transform Methods in Higher-order Logic: A Survey

Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using transform methods to prove various properties of these systems, such as, transfer function, frequency response and stability, and to find out solutions of the differential/difference equations. The conventional techniques for performing the transform methods based analysis have been unable to provide an accurate analysis of these systems. Therefore, higher-order-logic theorem proving, a formal method, has been used for accurately analyzing systems based on transform methods. In this paper, we survey developments for transform methods based analysis in various higher-order-logic theorem provers and overview the corresponding real world case studies from the avionics, medicine and transportation domains that have been analyzed based on these developments.

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arXiv2020

Formal Verification of Cyber-Physical Systems using Theorem Proving (Invited Paper)

Due to major breakthroughs in software and engineering technologies, embedded systems are increasingly being utilized in areas ranging from aerospace and next-generation transportation systems, to smart grid and smart cities, to health care systems, and broadly speaking to what is known as Cyber-Physical Systems (CPS). A CPS is primarily composed of several electronic, communication and controller modules and some actuators and sensors. The mix of heterogeneous underlying smart technologies poses a number of technical challenges to the design and more severely to the verification of such complex infrastructure. In fact, a CPS shall adhere to strict safety, reliability, performance and security requirements, where one needs to capture both physical and random aspects of the various CPS modules and then analyze their interrelationship across interlinked continuous and discrete dynamics. Often times however, system bugs remain uncaught during the analysis and in turn cause unwanted scenarios that may have serious consequences in safety-critical applications. In this paper, we introduce some of the challenges surrounding the design and verification of contemporary CPS with the advent of smart technologies. In particular, we survey recent developments in the use of theorem proving, a formal method, for the modeling, analysis and verification of CPS, and overview some real world CPS case studies from the automotive, avionics and healthtech domains from system level to physical components.

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arXiv2020

FASiM: A Framework for Automatic Formal Analysis of Simulink Models of Linear Analog Circuits

Simulink is a graphical environment that is widely adapted for the modeling and the Laplace transform based analysis of linear analog circuits used in signal processing architectures. However, due to the involvement of the numerical algorithms of MATLAB in the analysis process, the analysis results cannot be termed as complete and accurate. Higher-order-logic theorem proving is a formal verification method that has been recently proposed to overcome these limitations for the modeling and the Laplace transform based analysis of linear analog circuits. However, the formal modeling of a system is not a straightforward task due to the lack of formal methods background for engineers working in the industry. Moreover, due to the undecidable nature of higher-order logic, the analysis generally requires a significant amount of user guidance in the manual proof process. In order to facilitate industrial engineers to formally analyze the linear analog circuits based on the Laplace transform, we propose a framework, FASiM, which allows automatically conducting the formal analysis of the Simulink models of linear analog circuits using the HOL Light theorem prover. For illustration, we use FASiM to formally analyze Simulink models of some commonly used linear analog filters, such as Sallen-key filters.

cs.LO↗

arXiv2019

Formal Analysis of the Biological Circuits using Higher-order-logic Theorem Proving

Synthetic Biology is an interdisciplinary field that utilizes well-established engineering principles, ranging from electrical, control and computer systems, for analyzing the biological systems, such as biological circuits, enzymes, pathways and controllers. Traditionally, these biological systems, i.e., the genetic circuits are analyzed using paper-and-pencil proofs and computer-based simulations techniques. However, these methods cannot provide accurate results due to their inherent limitations such as human error-proneness, round-off errors and the unverified algorithms present in the core of the tools, providing such analyses. In this paper, we propose to use higher-order-logic theorem proving as a complementary technique for analyzing these systems and thus overcome the above-mentioned issues. In particular, we propose a higher-order-logic theorem proving based framework to formally reason about the genetic circuits used in synthetic biology. The main idea is to, first, model the continuous dynamics of the genetic circuits using differential equations. The next step is to obtain the systems' transfer function from their corresponding block diagram representations. Finally, the transfer function based analysis of these differential equation based models is performed using the Laplace transform. To illustrate the practical utilization of our proposed framework, we formally analyze the genetic circuits of activated and repressed expressions of protein.

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arXiv2018

Formal Modeling of Robotic Cell Injection Systems in Higher-order Logic

Robotic cell injection is used for automatically delivering substances into a cell and is an integral component of drug development, genetic engineering and many other areas of cell biology. Traditionally, the correctness of functionality of these systems is ascertained using paper-and-pencil proof and computer simulation methods. However, the paper based proofs can be human-error prone and the simulation provides an incomplete analysis due to its sampling based nature and the inability to capture continuous behaviors in computer based models. Model checking has been recently advocated for the analysis of cell injection systems as well. However, it involves the discretization of the differential equations that are used for modeling the dynamics of the system and thus compromises on the completeness of the analysis as well. In this paper, we propose to use higher-order-logic theorem proving for the modeling and analysis of the dynamical behaviour of the robotic cell injection systems. The high expressiveness of the underlying logic allows us to capture the continuous details of the model in their true form. Then, the model can be analyzed using deductive reasoning within the sound core of a proof assistant.

cs.LO↗

arXiv2018

Formalization of Lerch's Theorem using HOL Light

The Laplace transform is an algebraic method that is widely used for analyzing physical systems by either solving the differential equations modeling their dynamics or by evaluating their transfer function. The dynamics of the given system are firstly modeled using differential equations and then Laplace transform is applied to convert these differential equations to their equivalent algebraic equations. These equations can further be simplified to either obtain the transfer function of the system or to find out the solution of the differential equations in frequency domain. Next, the uniqueness of the Laplace transform provides the solution of these differential equations in the time domain. The traditional Laplace transform based analysis techniques, i.e., paper-and-pencil proofs and computer simulation methods are error-prone due to their inherent limitations and thus are not suitable for the analysis of the systems. Higher-order-logic theorem proving can overcome these limitations of these techniques and can ascertain accurate analysis of the systems. In this paper, we extend our higher-order logic formalization of the Laplace transform, which includes the formal definition of the Laplace transform and verification of its various classical properties. One of the main contributions of the paper is the formalization of Lerch's theorem, which describes the uniqueness of the Laplace transform and thus plays a vital role in solving linear differential equations in the frequency domain. For illustration, we present the formal analysis of a $4$-$π$ soft error crosstalk model, which is widely used in nanometer technologies, such as, Integrated Circuits (ICs).

cs.LO↗

arXiv2018

Formal Analysis of Robotic Cell Injection Systems using Theorem Proving

Cell injection is an approach used for the delivery of small sample substances into a biological cell and is widely used in drug development, gene injection, intracytoplasmic sperm injection (ICSI) and in-virto fertilization (IVF). Robotic cell injection systems provide the automation of the process as opposed to the manual and semi-automated cell injection systems, which require expert operators and involve time consuming processes and also have lower success rates. The automation of the cell injection process is achieved by controlling the injection force and planning the motion of the injection pipette. Traditionally, these systems are analyzed using paper-and-pencil proof and computer simulation methods. However, the former is human-error prone and the later is based on the numerical algorithms, where the approximation of the mathematical expressions introduces inaccuracies in the analysis. Formal methods can overcome these limitations and thus provide an accurate analysis of the cell injection systems. Model checking, i.e., a state-based formal method, has been recently proposed for the analysis of these systems. However, it involves the discretization of the differential equations that are used for modeling the dynamics of the system and thus compromises on the completeness of the analysis of these safety-critical systems. In this paper, we propose to use higher-order-logic theorem proving, a deductive-reasoning based formal method, for the modeling and analysis of the dynamical behaviour of the robotic cell injection systems. The proposed analysis, based on the HOL Light theorem prover, enabled us to identify some discrepancies in the simulation and model checking based analysis of the same robotic cell injection system.

cs.LO↗

arXiv2018

Formal Verification of Platoon Control Strategies

Recent developments in autonomous driving, vehicle-to-vehicle communication and smart traffic controllers have provided a hope to realize platoon formation of vehicles. The main benefits of vehicle platooning include improved safety, enhanced highway utility, efficient fuel consumption and reduced highway accidents. One of the central components of reliable and efficient platoon formation is the underlying control strategies, e.g., constant spacing, variable spacing and dynamic headway. In this paper, we provide a generic formalization of platoon control strategies in higher-order logic. In particular, we formally verify the stability constraints of various strategies using the libraries of multivariate calculus and Laplace transform within the sound core of HOL Light proof assistant. We also illustrate the use of verified stability theorems to develop runtime monitors for each controller, which can be used to automatically detect the violation of stability constraints in a runtime execution or a logged trace of the platoon controller. Our proposed formalization has two main advantages: 1) it provides a framework to combine both static (theorem proving) and dynamic (runtime) verification approaches for platoon controllers, and 2) it is inline with the industrial standards, which explicitly recommend the use of formal methods for functional safety, e.g., automotive ISO 26262.

cs.LO↗

arXiv2017

Formal Analysis of Continuous-time Systems using Fourier Transform

To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems. Traditionally, Fourier transform methods are used to perform this frequency domain analysis using paper-and-pencil based analytical techniques or computer simulations. However, both of these methods are error prone and thus are not suitable for analyzing systems used in safety-critical domains, like medicine and transportation. In order to provide an accurate alternative, we propose to use higher-order-logic theorem proving to conduct the frequency domain analysis of these systems. For this purpose, the paper presents a higher-order-logic formalization of Fourier transform using the HOL-Light theorem prover. In particular, we use the higher-order-logic based formalizations of differential, integral, transcendental and topological theories of multivariable calculus to formally define Fourier transform and reason about the correctness of its classical properties, such as existence, linearity, time shifting, frequency shifting, modulation, time scaling, time reversal and differentiation in time domain, and its relationships with Fourier Cosine, Fourier Sine and Laplace transforms. We use our proposed formalization for the formal verification of the frequency response of a generic n-order linear system, an audio equalizer and a MEMs accelerometer, using the HOL-Light theorem prover.

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arXiv2017

Formal Analysis of Linear Control Systems using Theorem Proving

Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation methods, however, both of these methods cannot provide accurate analysis due to their inherent limitations. Model checking has been widely used to analyze control systems but the continuous nature of their environment and physical components cannot be truly captured by a state-transition system in this technique. To overcome these limitations, we propose to use higher-order-logic theorem proving for analyzing linear control systems based on a formalized theory of the Laplace transform method. For this purpose, we have formalized the foundations of linear control system analysis in higher-order logic so that a linear control system can be readily modeled and analyzed. The paper presents a new formalization of the Laplace transform and the formal verification of its properties that are frequently used in the transfer function based analysis to judge the frequency response, gain margin and phase margin, and stability of a linear control system. We also formalize the active realizations of various controllers, like Proportional-Integral-Derivative (PID), Proportional-Integral (PI), Proportional-Derivative (PD), and various active and passive compensators, like lead, lag and lag-lead. For illustration, we present a formal analysis of an unmanned free-swimming submersible vehicle using the HOL Light theorem prover.

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