Classifying the computational power of stochastic physical oracles

Consider a computability and complexity theory in which the classical set-theoretic oracle to a Turing machine is replaced by a physical process, and oracle queries return measurements of physical behaviour. The idea of such physical oracles is relevant to many disparate situations, but research has focussed on physical oracles that were classic deterministic experiments which measure physical quantities. In this paper, we broaden the scope of the theory of physical oracles by tackling non-deterministic systems. We examine examples of three types of non-determinism, namely systems that are: (1) physically nondeterministic, as in quantum phenomena; (2) physically deterministic but whose physical theory is non-deterministic, as in statistical mechanics; and (3) physically deterministic but whose computational theory is non-deterministic caused by error margins. Physical oracles that have probabilistic theories we call stochastic physical oracles. We propose a set SPO of axioms for a basic form of stochastic oracles. We prove that Turing machines equipped with a physical oracle satisfying the axioms SPO compute precisely the non-uniform complexity class BPP//log* in polynomial time. This result of BPP/log* is a computational limit to a great range of classical and non-classical measurement, and of analogue-digital computation in polynomial time under general conditions.info:eu-repo/semantics/publishedVersio

Classifying the computational power of stochastic physical oracles

Consider a computability and complexity theory in which theclassical set-theoretic oracle to a Turing machine is replaced bya physical process, and oracle queries return measurements ofphysical behaviour. The idea of such physical oracles is relevantto many disparate situations, but research has focussed on physicaloracles that were classic deterministic experiments whichmeasure physical quantities. In this paper, we broaden the scopeof the theory of physical oracles by tackling non-deterministicsystems. We examine examples of three types of non-determinism,namely systems that are: (1) physically nondeterministic,as in quantum phenomena; (2) physically deterministic butwhose physical theory is non-deterministic, as in statistical mechanics;and (3) physically deterministic but whose computationaltheory is non-deterministic caused by error margins. Physicaloracles that have probabilistic theories we call stochasticphysical oracles. We propose a set SPO of axioms for a basicform of stochastic oracles. We prove that Turing machinesequipped with a physical oracle satisfying the axioms SPO computeprecisely the non-uniform complexity class BPP//log* inpolynomial time. This result of BPP//log* is a computationallimit to a great range of classical and non-classical measurement,and of analogue-digital computation in polynomial time undergeneral conditions

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers

28th International Symposium on Temporal Representation and Reasoning (TIME 2021)

The 28th International Symposium on Temporal Representation and Reasoning (TIME 2021) was planned to take place in Klagenfurt, Austria, but had to move to an online conference due to the insecurities and restrictions caused by the pandemic. Since its frst edition in 1994, TIME Symposium is quite unique in the panorama of the scientifc conferences as its main goal is to bring together researchers from distinct research areas involving the management and representation of temporal data as well as the reasoning about temporal aspects of information. Moreover, TIME Symposium aims to bridge theoretical and applied research, as well as to serve as an interdisciplinary forum for exchange among researchers from the areas of artifcial intelligence, database management, logic and verifcation, and beyond

Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing