perform complexity analysis

Traditional asymptotic complexity analysis (e.g., Big-O notation) lacks discriminative power among algorithms within the same asymptotic class. To address this, we propose *r-Complexity*, an architecture-aware, fine-grained asymptotic metric framework. Our method integrates an enhanced complexity calculus model with discrete analysis techniques to explicitly incorporate processor-specific characteristics—such as cache hierarchy and instruction throughput—into runtime modeling, thereby overcoming the limitation of Bachmann–Landau notation, which considers only input size growth. Unlike classical approaches, r-Complexity enables effective differentiation of practical performance among algorithms sharing the same asymptotic complexity (e.g., all O(n log n) algorithms). It significantly improves sensitivity, predictive accuracy, and engineering utility of complexity assessment, offering a more realistic and actionable basis for algorithm selection and system design.

Conventional algorithm analysis treats basic operations as equally costly, ignoring substantial disparities in execution time, energy consumption, carbon emissions, and monetary cost across modern processor architectures. Method: We propose a multidimensional weighted operation complexity model that unifies computational cost, energy usage, carbon footprint, and financial expense—enabling architecture-aware, sustainability-oriented algorithm evaluation. Our approach integrates instruction-level fine-grained cost modeling, automated source-code analysis, and empirical measurement tooling, supporting user-defined weight configurations for diverse optimization objectives. Contribution/Results: Experiments demonstrate strong correlation with ground-truth measurements (Spearman ρ > 0.9) and significantly higher prediction accuracy for runtime and energy than baseline methods—including Big-O, ICE, and EVM gas metrics. The model establishes a novel, interpretable, cross-architectural paradigm for algorithmic efficiency assessment in green computing and resource-constrained environments.

This work addresses automatic runtime and variable-size bound analysis for integer programs, focusing on the decidable subclass of periodic rational-solvable loops (PRS-loops). The proposed method introduces a modular analysis framework: it first derives local bounds for PRS-loops, then lifts them to global bounds via program transformation and inductive reasoning. Crucially, it extends the decidability of PRS-loop analysis to arbitrary integer programs by designing a synergistic synthesis mechanism combining abstract interpretation with rational linear algebra. The approach is fully automated in the tool KoAT, supporting precise derivation of polynomial and exponential complexity bounds as well as variable growth bounds. Experimental evaluation demonstrates effectiveness on diverse nontrivial integer programs, significantly improving the completeness, precision, and practicality of automated complexity analysis.

Existing approaches to program resource analysis struggle to simultaneously achieve the completeness of static analysis and the worst-case coverage afforded by dynamic analysis. To address this limitation, this work proposes a hybrid analysis method that integrates dynamic symbolic execution with mixed-integer linear programming to systematically enumerate execution paths within a bounded input space and derive empirically sound upper bounds on maximum resource consumption. This approach represents the first deep integration of dynamic symbolic execution and linear programming for inferring tight and effective worst-case resource bounds for functional programs. The prototype tool CompAS demonstrates both practical utility and theoretical guarantees in estimating resource usage on complex programs.

This paper addresses two major bottlenecks—excessive work and scattered output memory—in parallel evaluation of relational queries on the CRCW PRAM model. We propose the first constant-time, weakly work-efficient (O(T^{1+ε})) parallel evaluation framework. Methodologically, we integrate the Goldberg–Zwick approximate prefix-sum algorithm with compactification techniques, leveraging practical assumptions such as sorting or numerical constraints to achieve operator-level parallelization for acyclic queries, semijoin algebra, and worst-case-optimal joins. Our contributions are threefold: (i) the first constant-time, weakly work-efficient parallel evaluation for these three fundamental query classes; (ii) work complexity asymptotically approaching that of the optimal sequential algorithms; and (iii) substantial improvements over naive parallel approaches, coupled with highly compact output memory layout.

Network design entails trade-offs among quantitative attributes such as bandwidth, latency, and resilience, yet efficient analytical tools for such multi-objective reasoning remain scarce. This work proposes weighted Symbolic Packet Programs (wSPP) and trajectory-carrying Pareto semirings, grounded in weighted NetKAT, to compactly represent network policy semantics via symbolic data structures and enable joint computation of multi-objective Pareto fronts along with their corresponding paths. The approach integrates symbolic execution, a customized Kleene star algorithm, and semiring-based parametric modeling; its core implementation is written in Rust, with formal verification conducted in Lean. Experimental results demonstrate that the method matches KATch in Boolean reachability analysis, outperforms McNetKAT and Storm by several orders of magnitude in probabilistic analysis, and successfully supports multi-objective comparisons on Fat-tree and Jellyfish topologies.

This work investigates how to distinguish “easy” from “hard” input distributions in the stochastic caching problem to overcome the limitations imposed by worst-case analysis. To this end, we introduce subset entropy—a concept from information theory—as a novel parameter that enables the first fine-grained quantification of input distribution complexity. Building upon this measure, we develop a unified analytical framework applicable to both online and stochastic optimization settings. Within this framework, we establish competitive ratio upper bounds for classical algorithms such as LRU that explicitly depend on subset entropy. Our results demonstrate that under low-entropy distributions, these algorithms achieve substantially better performance than their classical worst-case guarantees, thereby providing new theoretical justification for the empirical effectiveness of LRU under realistic, structured inputs.

This work proposes a compositional and modular automated reasoning framework for simultaneously deriving upper bounds on runtime and proving termination of integer programs with recursion. The approach employs an alternating modular strategy that iteratively infers upper bounds on both the runtime and variable ranges of subroutines, seamlessly integrating multiple static analysis techniques to handle recursive calls and complex control flow. Experimental evaluation demonstrates that the framework substantially outperforms existing tools on large-scale benchmarks, exhibiting both high efficiency and strong scalability in automated complexity analysis and termination verification.