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Farkas certificates and minimal witnesses for probabilistic reachability constraints [article]

Florian Funke, Simon Jantsch, Christel Baier
2020 arXiv   pre-print
This paper introduces Farkas certificates for lower and upper bounds on minimal and maximal reachability probabilities in Markov decision processes (MDP), which we derive using an MDP-variant of Farkas  ...  The set of all such certificates is shown to form a polytope whose points correspond to witnessing subsystems of the model and the property.  ...  Relating Farkas certificates and minimal witnesses In this section we establish a strong connection between Farkas certificates on the one hand and witnesses for probabilistic reachability constraints  ... 
arXiv:1910.10636v2 fatcat:vnjjvropcbdznoptcri5fgkzpa

Farkas Certificates and Minimal Witnesses for Probabilistic Reachability Constraints [chapter]

Florian Funke, Simon Jantsch, Christel Baier
2020 Lecture Notes in Computer Science  
This paper introduces Farkas certificates for lower and upper bounds on minimal and maximal reachability probabilities in Markov decision processes (MDP), which we derive using an MDP-variant of Farkas  ...  The set of all such certificates is shown to form a polytope whose points correspond to witnessing subsystems of the model and the property.  ...  Relating Farkas certificates and minimal witnesses In this section we establish a strong connection between Farkas certificates on the one hand and witnesses for probabilistic reachability constraints  ... 
doi:10.1007/978-3-030-45190-5_18 fatcat:wvgpvvi2hzhrpbuv6gfl3wodp4

Minimal witnesses for probabilistic timed automata [article]

Simon Jantsch, Florian Funke, Christel Baier
2020 arXiv   pre-print
This paper introduces witnessing subsystems for reachability problems in probabilistic timed automata (PTA).  ...  We present algorithms for the computation of minimal witnessing subsystems under three notions of minimality, which capture the timed behavior from different perspectives, and discuss their complexity.  ...  The following proposition states that Farkas certificates for any PTAB quotient of the PTA can be used to find witnesses for probabilistic reachability constraints.  ... 
arXiv:2007.00637v1 fatcat:6i2mhwaqnjgnpbixh46s3bwyne

SWITSS: Computing Small Witnessing Subsystems [article]

Simon Jantsch, Hans Harder, Florian Funke, Christel Baier
2020 arXiv   pre-print
Witnessing subsystems for probabilistic reachability thresholds in discrete Markovian models are an important concept both as diagnostic information on why a property holds, and as input to refinement  ...  Returned subsystems can automatically be rendered graphically and are accompanied with a certificate which proves that the subsystem is indeed a witness.  ...  TABLE I : I Overview of Farkas certificates for reachability properties in MDPs, where ∈ {≤, <} and ∈ {≥, >}.  ... 
arXiv:2008.04049v1 fatcat:6bwert5vwng7dha5nlb7bog3jm

Ranking and Repulsing Supermartingales for Reachability in Probabilistic Programs [article]

Toru Takisaka, Yuichiro Oyabu, Natsuki Urabe, Ichiro Hasuo
2018 arXiv   pre-print
This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating reachability probabilities.  ...  Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs.  ...  An approach that is widely used in the literature is to use ranking supermartingales-a probabilistic analogue of ranking functions-as a witness for the qualitative question of almost-sure reachability.  ... 
arXiv:1805.10749v2 fatcat:6jbm445jpnfhnpgvzvmz72mprm

On Lexicographic Proof Rules for Probabilistic Termination [article]

Krishnendu Chatterjee, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, Đorđe Žikelić
2021 arXiv   pre-print
Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking  ...  We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs.  ...  This is done by fixing an LEM template for each location ℓ in C, and converting the above constraints to an equivalent linear program LP T in template variables via Farkas' lemma (FL).  ... 
arXiv:2108.02188v1 fatcat:5xnql7jo6bcatbw2t3stsics5q

Learning Probabilistic Termination Proofs [chapter]

Alessandro Abate, Mirco Giacobbe, Diptarko Roy
2021 Lecture Notes in Computer Science  
The result is thus a sound witness of probabilistic termination.  ...  Our learning strategy is agnostic to the source code and its verification counterpart supports the widest range of probabilistic single-loop programs that any existing tool can handle to date.  ...  For instance, methods that convert the RSM constraints into a linear program using Farkas' lemma can only handle programs with affine arithmetic, and can only synthesise linear/affine (lexicographic) RSMs  ... 
doi:10.1007/978-3-030-81688-9_1 fatcat:srgow3ul6ncypi5hkzdiwstovq

SWITSS: Computing Small Witnessing Subsystems [article]

Simon Jantsch, Hans Harder, Florian Funke, Christel Baier, Alexander Ivrii, Ofer Strichman
2020
Witnessing subsystems for probabilistic reachability thresholds in discrete Markovian models are an important concept both as diagnostic information on why a property holds, and as input to refinement  ...  Returned subsystems can automatically be rendered graphically and are accompanied with a certificate which proves that the subsystem is indeed a witness.  ...  TABLE I : I Overview of Farkas certificates for reachability properties in MDPs, where ∈ {≤, <} and ∈ {≥, >}.  ... 
doi:10.34727/2020/isbn.978-3-85448-042-6_31 fatcat:67lrmtpbkrfq5chnocunvtvi54

Polynomial Invariant Generation for Non-deterministic Recursive Programs [article]

Krishnendu Chatterjee and Hongfei Fu and Amir Kafshdar Goharshady and Ehsan Kafshdar Goharshady
2020 arXiv   pre-print
We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities.  ...  To the best of our knowledge, this is the first invariant generation method to provide completeness guarantees for invariants consisting of polynomial inequalities.  ...  for every reachable stack element (f , ℓ, ν ), it holds that ν |= Inv(ℓ).  ... 
arXiv:1902.04373v3 fatcat:bduo7cdmerb4rcs7v3vifn3voa

Decision algorithms for modelling, optimal control and verification of probabilistic systems [article]

Vahid Hashemi, Universität Des Saarlandes, Universität Des Saarlandes
2018
Moreover, we consider the problem of computing maximal/minimal reward-bounded reachability probabilities on UwMDPs, for which we present an efficient algorithm running in pseudo-polynomial time.  ...  Markov Decision Processes (MDPs) constitute a mathematical framework for modelling systems featuring both probabilistic and nondeterministic behaviour.  ...  Acknowledgments Throughout my amazing journey towards shaping this dissertation, I have been quite for-  ... 
doi:10.22028/d291-27039 fatcat:pceqvyd5zrfzbkgpkfov7k7pwm

Learning control lyapunov functions from counterexamples and demonstrations

Hadi Ravanbakhsh, Sriram Sankaranarayanan
2018 Autonomous Robots  
We also implement this scheme using nonlinear MPC controllers to serve as demonstrators for a set of state and trajectory stabilization problems for nonlinear dynamical systems.  ...  We present a technique for learning control Lyapunov-like functions, which are used in turn to synthesize controllers for nonlinear dynamical systems that can stabilize the system, or satisfy specifications  ...  Then, the approach repeatedly alternates between the following steps: 1. c is fixed, and we search for a θ that minimizes γ. 2. θ is fixed, and we search for a c that minimizes γ.  ... 
doi:10.1007/s10514-018-9791-9 fatcat:76lfjdwjkbcixoaw6qw57evhka

Proceedings of Formal Methods in Computer-Aided Design, FMCAD 2015 [article]

Formal Methods In Computer Aided Design
2016
FMCAD covers the spectrum of formal aspects of specification, verification, synthesis, and testing, and is intended as a leading forum for researchers and practitioners in academia and industry alike.  ...  The International Conference on Formal Methods in Computer-Aided Design (FMCAD) is a series of meetings presenting groundbreaking results on the theory and application of rigorous formal techniques for  ...  ACKNOWLEDGMENTS In the future, we plan to consider joining the two notions of refinement used in RAReQS and CAQE and to integrate our algorithm in a certification framework like [32] to enable its use  ... 
doi:10.15781/t23x83p30 fatcat:7m76yewhwnbjfizkm4jnav5xeq

Robot tour planning with high determination costs [article]

Wolfgang A. Welz, Technische Universität Berlin, Technische Universität Berlin, Martin Skutella
2014
In this context we propose a constraint integer programming formulation that efficiently integrates the robot motion planning into a branch-and-price approach for the underlying routing problem.  ...  The automotive industry of today is characterized by an increasing importance of computerization and robotic automation.  ...  For example, the sequencing and assignment both depend on the distances between all reachable weld points.  ... 
doi:10.14279/depositonce-4300 fatcat:toiromk3jnhr5mbrqgygywfj6q

What makes quantum clicks special? [article]

Karl Svozil
2020 arXiv   pre-print
This is an elaboration about the "extra" advantage of the performance of quantized physical systems over classical ones; both in terms of single outcomes as well as probabilistic predictions.  ...  From a formal point of view, it is based upon entities related to (dual) vectors in (dual) Hilbert spaces, as compared to the Boolean algebra of subsets of a set and the additive measures they support.  ...  By taking the minimal and the maximal eigenvalue in the spectral sum of this comprehensive observable one, therefore, obtains the minimal and the maximal measurement outcomes "reachable" by quantization  ... 
arXiv:1707.08915v4 fatcat:hy4q3o4qrjhv5jymn3uzuldc2u

Quantum Mechanics in a Nutshell [chapter]

Karl Svozil
2018 Physical (A)Causality  
Both von Neumann and Everett called the former, irreversible, discontinuous change the "process 1"; and the latter, reversible, continuous, deterministic change the "process 2," respectively.  ...  It includes reversible as well as irreversible processes, and is prima facie inconsistent.  ...  By taking the minimal and the maximal eigenvalue in the spectral sum of this comprehensive observable one therefore obtains the minimal and the maximal measurement outcomes "reachable" by quantization.  ... 
doi:10.1007/978-3-319-70815-7_12 fatcat:uhdtagzasrge3ayz4jiqumep34
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