@misc{5439, abstract = {The target discounted-sum problem is the following: Given a rational discount factor 0 < λ < 1 and three rational values a, b, and t, does there exist a finite or an infinite sequence w ε(a, b)∗ or w ε(a, b)w, such that Σ|w| i=0 w(i)λi equals t? The problem turns out to relate to many fields of mathematics and computer science, and its decidability question is surprisingly hard to solve. We solve the finite version of the problem, and show the hardness of the infinite version, linking it to various areas and open problems in mathematics and computer science: β-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set. We provide some partial results to the infinite version, among which are solutions to its restriction to eventually-periodic sequences and to the cases that λ λ 1/2 or λ = 1/n, for every n ε N. We use our results for solving some open problems on discounted-sum automata, among which are the exact-value problem for nondeterministic automata over finite words and the universality and inclusion problems for functional automata. }, author = {Boker, Udi and Henzinger, Thomas A and Otop, Jan}, issn = {2664-1690}, pages = {20}, publisher = {IST Austria}, title = {{The target discounted-sum problem}}, doi = {10.15479/AT:IST-2015-335-v1-1}, year = {2015}, } @misc{5549, abstract = {This repository contains the experimental part of the CAV 2015 publication Counterexample Explanation by Learning Small Strategies in Markov Decision Processes. We extended the probabilistic model checker PRISM to represent strategies of Markov Decision Processes as Decision Trees. The archive contains a java executable version of the extended tool (prism_dectree.jar) together with a few examples of the PRISM benchmark library. To execute the program, please have a look at the README.txt, which provides instructions and further information on the archive. The archive contains scripts that (if run often enough) reproduces the data presented in the publication.}, author = {Fellner, Andreas}, keywords = {Markov Decision Process, Decision Tree, Probabilistic Verification, Counterexample Explanation}, publisher = {Institute of Science and Technology Austria}, title = {{Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes}}, doi = {10.15479/AT:ISTA:28}, year = {2015}, } @inproceedings{1729, abstract = {We present a computer-aided programming approach to concurrency. The approach allows programmers to program assuming a friendly, non-preemptive scheduler, and our synthesis procedure inserts synchronization to ensure that the final program works even with a preemptive scheduler. The correctness specification is implicit, inferred from the non-preemptive behavior. Let us consider sequences of calls that the program makes to an external interface. The specification requires that any such sequence produced under a preemptive scheduler should be included in the set of such sequences produced under a non-preemptive scheduler. The solution is based on a finitary abstraction, an algorithm for bounded language inclusion modulo an independence relation, and rules for inserting synchronization. We apply the approach to device-driver programming, where the driver threads call the software interface of the device and the API provided by the operating system. Our experiments demonstrate that our synthesis method is precise and efficient, and, since it does not require explicit specifications, is more practical than the conventional approach based on user-provided assertions.}, author = {Cerny, Pavol and Clarke, Edmund and Henzinger, Thomas A and Radhakrishna, Arjun and Ryzhyk, Leonid and Samanta, Roopsha and Tarrach, Thorsten}, location = {San Francisco, CA, United States}, pages = {180 -- 197}, publisher = {Springer}, title = {{From non-preemptive to preemptive scheduling using synchronization synthesis}}, doi = {10.1007/978-3-319-21668-3_11}, volume = {9207}, year = {2015}, } @inproceedings{1502, abstract = {We extend the theory of input-output conformance with operators for merge and quotient. The former is useful when testing against multiple requirements or views. The latter can be used to generate tests for patches of an already tested system. Both operators can combine systems with different action alphabets, which is usually the case when constructing complex systems and specifications from parts, for instance different views as well as newly defined functionality of a~previous version of the system.}, author = {Beneš, Nikola and Daca, Przemyslaw and Henzinger, Thomas A and Kretinsky, Jan and Nickovic, Dejan}, isbn = {978-1-4503-3471-6}, location = {Montreal, QC, Canada}, pages = {101 -- 110}, publisher = {ACM}, title = {{Complete composition operators for IOCO-testing theory}}, doi = {10.1145/2737166.2737175}, year = {2015}, } @article{1501, abstract = {We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph algorithms with quadratic complexity to compute the simulation relation. We present an automated technique for assume-guarantee style reasoning for compositional analysis of two-player games by giving a counterexample guided abstraction-refinement approach to compute our new simulation relation. We show a tight link between two-player games and MDPs, and as a consequence the results for games are lifted to MDPs with qualitative properties. We have implemented our algorithms and show that the compositional analysis leads to significant improvements. }, author = {Chatterjee, Krishnendu and Chmelik, Martin and Daca, Przemyslaw}, journal = {Formal Methods in System Design}, number = {2}, pages = {230 -- 264}, publisher = {Springer}, title = {{CEGAR for compositional analysis of qualitative properties in Markov decision processes}}, doi = {10.1007/s10703-015-0235-2}, volume = {47}, year = {2015}, } @inproceedings{1610, abstract = {The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1,L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to pushdown automata is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Ibsen-Jensen, Rasmus and Otop, Jan}, booktitle = {42nd International Colloquium on Automata, Languages, and Programming}, isbn = {978-3-662-47665-9}, location = {Kyoto, Japan}, number = {Part II}, pages = {121 -- 133}, publisher = {Springer Nature}, title = {{Edit distance for pushdown automata}}, doi = {10.1007/978-3-662-47666-6_10}, volume = {9135}, year = {2015}, } @inproceedings{1392, abstract = {Fault-tolerant distributed algorithms play an important role in ensuring the reliability of many software applications. In this paper we consider distributed algorithms whose computations are organized in rounds. To verify the correctness of such algorithms, we reason about (i) properties (such as invariants) of the state, (ii) the transitions controlled by the algorithm, and (iii) the communication graph. We introduce a logic that addresses these points, and contains set comprehensions with cardinality constraints, function symbols to describe the local states of each process, and a limited form of quantifier alternation to express the verification conditions. We show its use in automating the verification of consensus algorithms. In particular, we give a semi-decision procedure for the unsatisfiability problem of the logic and identify a decidable fragment. We successfully applied our framework to verify the correctness of a variety of consensus algorithms tolerant to both benign faults (message loss, process crashes) and value faults (message corruption).}, author = {Dragoi, Cezara and Henzinger, Thomas A and Veith, Helmut and Widder, Josef and Zufferey, Damien}, location = {San Diego, USA}, pages = {161 -- 181}, publisher = {Springer}, title = {{A logic-based framework for verifying consensus algorithms}}, doi = {10.1007/978-3-642-54013-4_10}, volume = {8318}, year = {2014}, } @inproceedings{1393, abstract = {Probabilistic programs are usual functional or imperative programs with two added constructs: (1) the ability to draw values at random from distributions, and (2) the ability to condition values of variables in a program via observations. Models from diverse application areas such as computer vision, coding theory, cryptographic protocols, biology and reliability analysis can be written as probabilistic programs. Probabilistic inference is the problem of computing an explicit representation of the probability distribution implicitly specified by a probabilistic program. Depending on the application, the desired output from inference may vary-we may want to estimate the expected value of some function f with respect to the distribution, or the mode of the distribution, or simply a set of samples drawn from the distribution. In this paper, we describe connections this research area called \Probabilistic Programming" has with programming languages and software engineering, and this includes language design, and the static and dynamic analysis of programs. We survey current state of the art and speculate on promising directions for future research.}, author = {Gordon, Andrew and Henzinger, Thomas A and Nori, Aditya and Rajamani, Sriram}, booktitle = {Proceedings of the on Future of Software Engineering}, location = {Hyderabad, India}, pages = {167 -- 181}, publisher = {ACM}, title = {{Probabilistic programming}}, doi = {10.1145/2593882.2593900}, year = {2014}, } @inproceedings{1869, abstract = {Boolean controllers for systems with complex datapaths are often very difficult to implement correctly, in particular when concurrency is involved. Yet, in many instances it is easy to formally specify correctness. For example, the specification for the controller of a pipelined processor only has to state that the pipelined processor gives the same results as a non-pipelined reference design. This makes such controllers a good target for automated synthesis. However, an efficient abstraction for the complex datapath elements is needed, as a bit-precise description is often infeasible. We present Suraq, the first controller synthesis tool which uses uninterpreted functions for the abstraction. Quantified firstorder formulas (with specific quantifier structure) serve as the specification language from which Suraq synthesizes Boolean controllers. Suraq transforms the specification into an unsatisfiable SMT formula, and uses Craig interpolation to compute its results. Using Suraq, we were able to synthesize a controller (consisting of two Boolean signals) for a five-stage pipelined DLX processor in roughly one hour and 15 minutes.}, author = {Hofferek, Georg and Gupta, Ashutosh}, booktitle = {HVC 2014}, editor = {Yahav, Eran}, location = {Haifa, Israel}, pages = {68 -- 74}, publisher = {Springer}, title = {{Suraq - a controller synthesis tool using uninterpreted functions}}, doi = {10.1007/978-3-319-13338-6_6}, volume = {8855}, year = {2014}, } @inproceedings{1870, abstract = {We investigate the problem of checking if a finite-state transducer is robust to uncertainty in its input. Our notion of robustness is based on the analytic notion of Lipschitz continuity - a transducer is K-(Lipschitz) robust if the perturbation in its output is at most K times the perturbation in its input. We quantify input and output perturbation using similarity functions. We show that K-robustness is undecidable even for deterministic transducers. We identify a class of functional transducers, which admits a polynomial time automata-theoretic decision procedure for K-robustness. This class includes Mealy machines and functional letter-to-letter transducers. We also study K-robustness of nondeterministic transducers. Since a nondeterministic transducer generates a set of output words for each input word, we quantify output perturbation using setsimilarity functions. We show that K-robustness of nondeterministic transducers is undecidable, even for letter-to-letter transducers. We identify a class of set-similarity functions which admit decidable K-robustness of letter-to-letter transducers.}, author = {Henzinger, Thomas A and Otop, Jan and Samanta, Roopsha}, booktitle = {Leibniz International Proceedings in Informatics, LIPIcs}, location = {Delhi, India}, pages = {431 -- 443}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Lipschitz robustness of finite-state transducers}}, doi = {10.4230/LIPIcs.FSTTCS.2014.431}, volume = {29}, year = {2014}, } @inproceedings{1872, abstract = {Extensionality axioms are common when reasoning about data collections, such as arrays and functions in program analysis, or sets in mathematics. An extensionality axiom asserts that two collections are equal if they consist of the same elements at the same indices. Using extensionality is often required to show that two collections are equal. A typical example is the set theory theorem (∀x)(∀y)x∪y = y ∪x. Interestingly, while humans have no problem with proving such set identities using extensionality, they are very hard for superposition theorem provers because of the calculi they use. In this paper we show how addition of a new inference rule, called extensionality resolution, allows first-order theorem provers to easily solve problems no modern first-order theorem prover can solve. We illustrate this by running the VAMPIRE theorem prover with extensionality resolution on a number of set theory and array problems. Extensionality resolution helps VAMPIRE to solve problems from the TPTP library of first-order problems that were never solved before by any prover.}, author = {Gupta, Ashutosh and Kovács, Laura and Kragl, Bernhard and Voronkov, Andrei}, booktitle = {ATVA 2014}, editor = {Cassez, Franck and Raskin, Jean-François}, location = {Sydney, Australia}, pages = {185 -- 200}, publisher = {Springer}, title = {{Extensional crisis and proving identity}}, doi = {10.1007/978-3-319-11936-6_14}, volume = {8837}, year = {2014}, } @inproceedings{2026, abstract = {We present a tool for translating LTL formulae into deterministic ω-automata. It is the first tool that covers the whole LTL that does not use Safra’s determinization or any of its variants. This leads to smaller automata. There are several outputs of the tool: firstly, deterministic Rabin automata, which are the standard input for probabilistic model checking, e.g. for the probabilistic model-checker PRISM; secondly, deterministic generalized Rabin automata, which can also be used for probabilistic model checking and are sometimes by orders of magnitude smaller. We also link our tool to PRISM and show that this leads to a significant speed-up of probabilistic LTL model checking, especially with the generalized Rabin automata.}, author = {Komárková, Zuzana and Kretinsky, Jan}, booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}, editor = {Cassez, Franck and Raskin, Jean-François}, location = {Sydney, Australia}, pages = {235 -- 241}, publisher = {Springer}, title = {{Rabinizer 3: Safraless translation of ltl to small deterministic automata}}, doi = {10.1007/978-3-319-11936-6_17}, volume = {8837}, year = {2014}, } @inproceedings{2027, abstract = {We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the state space. Our framework focuses on probabilistic reachability, which is a core property for verification, and is illustrated through two distinct instantiations. The first assumes that full knowledge of the MDP is available, and performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP, and yields probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. The latter is the first extension of statistical model checking for unbounded properties inMDPs. In contrast with other related techniques, our approach is not restricted to time-bounded (finite-horizon) or discounted properties, nor does it assume any particular properties of the MDP. We also show how our methods extend to LTL objectives. We present experimental results showing the performance of our framework on several examples.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Chmelik, Martin and Forejt, Vojtěch and Kretinsky, Jan and Kwiatkowska, Marta and Parker, David and Ujma, Mateusz}, booktitle = { Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}, editor = {Cassez, Franck and Raskin, Jean-François}, location = {Sydney, Australia}, pages = {98 -- 114}, publisher = {Springer}, title = {{Verification of markov decision processes using learning algorithms}}, doi = {10.1007/978-3-319-11936-6_8}, volume = {8837}, year = {2014}, } @article{2038, abstract = {Recently, there has been an effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions. At the heart of quantitative objectives lies the accumulation of values along a computation. It is often the accumulated sum, as with energy objectives, or the accumulated average, as with mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric (or Boolean) variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point in time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire infinite computation. We study the border of decidability for such quantitative extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities with both prefix-accumulation assertions, or extending LTL with both path-accumulation assertions, results in temporal logics whose model-checking problem is decidable. Moreover, the prefix-accumulation assertions may be generalized with "controlled accumulation," allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that this branching-time logic is, in a sense, the maximal logic with one or both of the prefix-accumulation assertions that permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, such as CTL or LTL, makes the problem undecidable.}, author = {Boker, Udi and Chatterjee, Krishnendu and Henzinger, Thomas A and Kupferman, Orna}, journal = {ACM Transactions on Computational Logic (TOCL)}, number = {4}, publisher = {ACM}, title = {{Temporal specifications with accumulative values}}, doi = {10.1145/2629686}, volume = {15}, year = {2014}, } @inproceedings{2053, abstract = {In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a longstanding open problem concerning the representation of memoryless continuous time by memoryfull continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems.}, author = {Hermanns, Holger and Krčál, Jan and Kretinsky, Jan}, booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}, editor = {Baldan, Paolo and Gorla, Daniele}, location = {Rome, Italy}, pages = {249 -- 265}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Probabilistic bisimulation: Naturally on distributions}}, doi = {10.1007/978-3-662-44584-6_18}, volume = {8704}, year = {2014}, } @article{2056, abstract = {We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.}, author = {Ganguly, Arnab and Petrov, Tatjana and Koeppl, Heinz}, journal = {Journal of Mathematical Biology}, number = {3}, pages = {767 -- 797}, publisher = {Springer}, title = {{Markov chain aggregation and its applications to combinatorial reaction networks}}, doi = {10.1007/s00285-013-0738-7}, volume = {69}, year = {2014}, } @inproceedings{1875, abstract = {We present a formal framework for repairing infinite-state, imperative, sequential programs, with (possibly recursive) procedures and multiple assertions; the framework can generate repaired programs by modifying the original erroneous program in multiple program locations, and can ensure the readability of the repaired program using user-defined expression templates; the framework also generates a set of inductive assertions that serve as a proof of correctness of the repaired program. As a step toward integrating programmer intent and intuition in automated program repair, we present a cost-aware formulation - given a cost function associated with permissible statement modifications, the goal is to ensure that the total program modification cost does not exceed a given repair budget. As part of our predicate abstractionbased solution framework, we present a sound and complete algorithm for repair of Boolean programs. We have developed a prototype tool based on SMT solving and used it successfully to repair diverse errors in benchmark C programs.}, author = {Samanta, Roopsha and Olivo, Oswaldo and Allen, Emerson}, editor = {Müller-Olm, Markus and Seidl, Helmut}, location = {Munich, Germany}, pages = {268 -- 284}, publisher = {Springer}, title = {{Cost-aware automatic program repair}}, doi = {10.1007/978-3-319-10936-7_17}, volume = {8723}, year = {2014}, } @article{2187, abstract = {Systems should not only be correct but also robust in the sense that they behave reasonably in unexpected situations. This article addresses synthesis of robust reactive systems from temporal specifications. Existing methods allow arbitrary behavior if assumptions in the specification are violated. To overcome this, we define two robustness notions, combine them, and show how to enforce them in synthesis. The first notion applies to safety properties: If safety assumptions are violated temporarily, we require that the system recovers to normal operation with as few errors as possible. The second notion requires that, if liveness assumptions are violated, as many guarantees as possible should be fulfilled nevertheless. We present a synthesis procedure achieving this for the important class of GR(1) specifications, and establish complexity bounds. We also present an implementation of a special case of robustness, and show experimental results.}, author = {Bloem, Roderick and Chatterjee, Krishnendu and Greimel, Karin and Henzinger, Thomas A and Hofferek, Georg and Jobstmann, Barbara and Könighofer, Bettina and Könighofer, Robert}, journal = {Acta Informatica}, number = {3-4}, pages = {193 -- 220}, publisher = {Springer}, title = {{Synthesizing robust systems}}, doi = {10.1007/s00236-013-0191-5}, volume = {51}, year = {2014}, } @inproceedings{2190, abstract = {We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula φ. The automaton is the product of a master automaton and an array of slave automata, one for each G-subformula of φ. The slave automaton for G ψ is in charge of recognizing whether FG ψ holds. As opposed to standard determinization procedures, the states of all our automata have a clear logical structure, which allows for various optimizations. Our construction subsumes former algorithms for fragments of LTL. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.}, author = {Esparza, Javier and Kretinsky, Jan}, pages = {192 -- 208}, publisher = {Springer}, title = {{From LTL to deterministic automata: A safraless compositional approach}}, doi = {10.1007/978-3-319-08867-9_13}, volume = {8559}, year = {2014}, } @inproceedings{2217, abstract = {As hybrid systems involve continuous behaviors, they should be evaluated by quantitative methods, rather than qualitative methods. In this paper we adapt a quantitative framework, called model measuring, to the hybrid systems domain. The model-measuring problem asks, given a model M and a specification, what is the maximal distance such that all models within that distance from M satisfy (or violate) the specification. A distance function on models is given as part of the input of the problem. Distances, especially related to continuous behaviors are more natural in the hybrid case than the discrete case. We are interested in distances represented by monotonic hybrid automata, a hybrid counterpart of (discrete) weighted automata, whose recognized timed languages are monotone (w.r.t. inclusion) in the values of parameters. The contributions of this paper are twofold. First, we give sufficient conditions under which the model-measuring problem can be solved. Second, we discuss the modeling of distances and applications of the model-measuring problem.}, author = {Henzinger, Thomas A and Otop, Jan}, booktitle = {Proceedings of the 17th international conference on Hybrid systems: computation and control}, location = {Berlin, Germany}, pages = {213 -- 222}, publisher = {Springer}, title = {{Model measuring for hybrid systems}}, doi = {10.1145/2562059.2562130}, year = {2014}, }