@article{3249, abstract = {Boolean notions of correctness are formalized by preorders on systems. Quantitative measures of correctness can be formalized by real-valued distance functions between systems, where the distance between implementation and specification provides a measure of "fit" or "desirability". We extend the simulation preorder to the quantitative setting by making each player of a simulation game pay a certain price for her choices. We use the resulting games with quantitative objectives to define three different simulation distances. The correctness distance measures how much the specification must be changed in order to be satisfied by the implementation. The coverage distance measures how much the implementation restricts the degrees of freedom offered by the specification. The robustness distance measures how much a system can deviate from the implementation description without violating the specification. We consider these distances for safety as well as liveness specifications. The distances can be computed in polynomial time for safety specifications, and for liveness specifications given by weak fairness constraints. We show that the distance functions satisfy the triangle inequality, that the distance between two systems does not increase under parallel composition with a third system, and that the distance between two systems can be bounded from above and below by distances between abstractions of the two systems. These properties suggest that our simulation distances provide an appropriate basis for a quantitative theory of discrete systems. We also demonstrate how the robustness distance can be used to measure how many transmission errors are tolerated by error correcting codes.}, author = {Cerny, Pavol and Henzinger, Thomas A and Radhakrishna, Arjun}, journal = {Theoretical Computer Science}, number = {1}, pages = {21 -- 35}, publisher = {Elsevier}, title = {{Simulation distances}}, doi = {10.1016/j.tcs.2011.08.002}, volume = {413}, year = {2012}, } @inproceedings{3251, abstract = {Many infinite state systems can be seen as well-structured transition systems (WSTS), i.e., systems equipped with a well-quasi-ordering on states that is also a simulation relation. WSTS are an attractive target for formal analysis because there exist generic algorithms that decide interesting verification problems for this class. Among the most popular algorithms are acceleration-based forward analyses for computing the covering set. Termination of these algorithms can only be guaranteed for flattable WSTS. Yet, many WSTS of practical interest are not flattable and the question whether any given WSTS is flattable is itself undecidable. We therefore propose an analysis that computes the covering set and captures the essence of acceleration-based algorithms, but sacrifices precision for guaranteed termination. Our analysis is an abstract interpretation whose abstract domain builds on the ideal completion of the well-quasi-ordered state space, and a widening operator that mimics acceleration and controls the loss of precision of the analysis. We present instances of our framework for various classes of WSTS. Our experience with a prototype implementation indicates that, despite the inherent precision loss, our analysis often computes the precise covering set of the analyzed system.}, author = {Zufferey, Damien and Wies, Thomas and Henzinger, Thomas A}, location = {Philadelphia, PA, USA}, pages = {445 -- 460}, publisher = {Springer}, title = {{Ideal abstractions for well structured transition systems}}, doi = {10.1007/978-3-642-27940-9_29}, volume = {7148}, year = {2012}, } @inproceedings{3253, abstract = {We describe a framework for reasoning about programs with lists carrying integer numerical data. We use abstract domains to describe and manipulate complex constraints on configurations of these programs mixing constraints on the shape of the heap, sizes of the lists, on the multisets of data stored in these lists, and on the data at their different positions. Moreover, we provide powerful techniques for automatic validation of Hoare-triples and invariant checking, as well as for automatic synthesis of invariants and procedure summaries using modular inter-procedural analysis. The approach has been implemented in a tool called Celia and experimented successfully on a large benchmark of programs.}, author = {Bouajjani, Ahmed and Dragoi, Cezara and Enea, Constantin and Sighireanu, Mihaela}, location = {Philadelphia, PA, USA}, pages = {1 -- 22}, publisher = {Springer}, title = {{Abstract domains for automated reasoning about list manipulating programs with infinite data}}, doi = {10.1007/978-3-642-27940-9_1}, volume = {7148}, year = {2012}, } @article{3836, abstract = {Hierarchical Timing Language (HTL) is a coordination language for distributed, hard real-time applications. HTL is a hierarchical extension of Giotto and, like its predecessor, based on the logical execution time (LET) paradigm of real-time programming. Giotto is compiled into code for a virtual machine, called the EmbeddedMachine (or E machine). If HTL is targeted to the E machine, then the hierarchicalprogram structure needs to be flattened; the flattening makes separatecompilation difficult, and may result in E machinecode of exponential size. In this paper, we propose a generalization of the E machine, which supports a hierarchicalprogram structure at runtime through real-time trigger mechanisms that are arranged in a tree. We present the generalized E machine, and a modular compiler for HTL that generates code of linear size. The compiler may generate code for any part of a given HTL program separately in any order.}, author = {Ghosal, Arkadeb and Iercan, Daniel and Kirsch, Christoph and Henzinger, Thomas A and Sangiovanni Vincentelli, Alberto}, journal = {Science of Computer Programming}, number = {2}, pages = {96 -- 112}, publisher = {Elsevier}, title = {{Separate compilation of hierarchical real-time programs into linear-bounded embedded machine code}}, doi = {10.1016/j.scico.2010.06.004}, volume = {77}, year = {2012}, } @article{3846, abstract = {We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems. Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not. We cluster known results and open problems according to these classifications.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A}, journal = {Journal of Computer and System Sciences}, number = {2}, pages = {394 -- 413}, publisher = {Elsevier}, title = {{A survey of stochastic ω regular games}}, doi = {10.1016/j.jcss.2011.05.002}, volume = {78}, year = {2012}, } @inproceedings{2942, abstract = {Interface theories provide a formal framework for component-based development of software and hardware which supports the incremental design of systems and the independent implementability of components. These capabilities are ensured through mathematical properties of the parallel composition operator and the refinement relation for components. More recently, a conjunction operation was added to interface theories in order to provide support for handling multiple viewpoints, requirements engineering, and component reuse. Unfortunately, the conjunction operator does not allow independent implementability in general. In this paper, we study conditions that need to be imposed on interface models in order to enforce independent implementability with respect to conjunction. We focus on multiple viewpoint specifications and propose a new compatibility criterion between two interfaces, which we call orthogonality. We show that orthogonal interfaces can be refined separately, while preserving both orthogonality and composability with other interfaces. We illustrate the independent implementability of different viewpoints with a FIFO buffer example.}, author = {Henzinger, Thomas A and Nickovic, Dejan}, booktitle = {Conference proceedings Monterey Workshop 2012}, location = {Oxford, UK}, pages = {380 -- 395}, publisher = {Springer}, title = {{Independent implementability of viewpoints}}, doi = {10.1007/978-3-642-34059-8_20}, volume = {7539}, year = {2012}, } @article{2967, abstract = {For programs whose data variables range over Boolean or finite domains, program verification is decidable, and this forms the basis of recent tools for software model checking. In this article, we consider algorithmic verification of programs that use Boolean variables, and in addition, access a single read-only array whose length is potentially unbounded, and whose elements range over an unbounded data domain. We show that the reachability problem, while undecidable in general, is (1) PSPACE-complete for programs in which the array-accessing for-loops are not nested, (2) decidable for a restricted class of programs with doubly nested loops. The second result establishes connections to automata and logics defining languages over data words.}, author = {Alur, Rajeev and Cerny, Pavol and Weinstein, Scott}, journal = {ACM Transactions on Computational Logic}, number = {3}, publisher = {ACM}, title = {{Algorithmic analysis of array-accessing programs}}, doi = {10.1145/2287718.2287727}, volume = {13}, year = {2012}, } @article{494, abstract = {We solve the longstanding open problems of the blow-up involved in the translations, when possible, of a nondeterministic Büchi word automaton (NBW) to a nondeterministic co-Büchi word automaton (NCW) and to a deterministic co-Büchi word automaton (DCW). For the NBW to NCW translation, the currently known upper bound is 2o(nlog n) and the lower bound is 1.5n. We improve the upper bound to n2n and describe a matching lower bound of 2ω(n). For the NBW to DCW translation, the currently known upper bound is 2o(nlog n). We improve it to 2 o(n), which is asymptotically tight. Both of our upper-bound constructions are based on a simple subset construction, do not involve intermediate automata with richer acceptance conditions, and can be implemented symbolically. We continue and solve the open problems of translating nondeterministic Streett, Rabin, Muller, and parity word automata to NCW and to DCW. Going via an intermediate NBW is not optimal and we describe direct, simple, and asymptotically tight constructions, involving a 2o(n) blow-up. The constructions are variants of the subset construction, providing a unified approach for translating all common classes of automata to NCW and DCW. Beyond the theoretical importance of the results, we point to numerous applications of the new constructions. In particular, they imply a simple subset-construction based translation, when possible, of LTL to deterministic Büchi word automata.}, author = {Boker, Udi and Kupferman, Orna}, journal = {ACM Transactions on Computational Logic}, number = {4}, publisher = {ACM}, title = {{Translating to Co-Büchi made tight, unified, and useful}}, doi = {10.1145/2362355.2362357}, volume = {13}, year = {2012}, } @inproceedings{2891, abstract = {Quantitative automata are nondeterministic finite automata with edge weights. They value a run by some function from the sequence of visited weights to the reals, and value a word by its minimal/maximal run. They generalize boolean automata, and have gained much attention in recent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and limit-average automata, cannot be determinized. Yet, the quantitative setting provides the potential of approximate determinization. We define approximate determinization with respect to a distance function, and investigate this potential. We show that sum automata cannot be determinized approximately with respect to any distance function. However, restricting to nonnegative weights allows for approximate determinization with respect to some distance functions. Discounted-sum automata allow for approximate determinization, as the influence of a word’s suffix is decaying. However, the naive approach, of unfolding the automaton computations up to a sufficient level, is shown to be doubly exponential in the discount factor. We provide an alternative construction that is singly exponential in the discount factor, in the precision, and in the number of states. We prove matching lower bounds, showing exponential dependency on each of these three parameters. Average and limit-average automata are shown to prohibit approximate determinization with respect to any distance function, and this is the case even for two weights, 0 and 1.}, author = {Boker, Udi and Henzinger, Thomas A}, booktitle = {Leibniz International Proceedings in Informatics}, location = {Hyderabad, India}, pages = {362 -- 373}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Approximate determinization of quantitative automata}}, doi = {10.4230/LIPIcs.FSTTCS.2012.362}, volume = {18}, year = {2012}, } @inproceedings{10906, abstract = {HSF(C) is a tool that automates verification of safety and liveness properties for C programs. This paper describes the verification approach taken by HSF(C) and provides instructions on how to install and use the tool.}, author = {Grebenshchikov, Sergey and Gupta, Ashutosh and Lopes, Nuno P. and Popeea, Corneliu and Rybalchenko, Andrey}, booktitle = {Tools and Algorithms for the Construction and Analysis of Systems}, editor = {Flanagan, Cormac and König, Barbara}, isbn = {9783642287558}, issn = {1611-3349}, location = {Tallinn, Estonia}, pages = {549--551}, publisher = {Springer}, title = {{HSF(C): A software verifier based on Horn clauses}}, doi = {10.1007/978-3-642-28756-5_46}, volume = {7214}, year = {2012}, } @article{531, abstract = {Software transactional memories (STM) are described in the literature with assumptions of sequentially consistent program execution and atomicity of high level operations like read, write, and abort. However, in a realistic setting, processors use relaxed memory models to optimize hardware performance. Moreover, the atomicity of operations depends on the underlying hardware. This paper presents the first approach to verify STMs under relaxed memory models with atomicity of 32 bit loads and stores, and read-modify-write operations. We describe RML, a simple language for expressing concurrent programs. We develop a semantics of RML parametrized by a relaxed memory model. We then present our tool, FOIL, which takes as input the RML description of an STM algorithm restricted to two threads and two variables, and the description of a memory model, and automatically determines the locations of fences, which if inserted, ensure the correctness of the restricted STM algorithm under the given memory model. We use FOIL to verify DSTM, TL2, and McRT STM under the memory models of sequential consistency, total store order, partial store order, and relaxed memory order for two threads and two variables. Finally, we extend the verification results for DSTM and TL2 to an arbitrary number of threads and variables by manually proving that the structural properties of STMs are satisfied at the hardware level of atomicity under the considered relaxed memory models.}, author = {Guerraoui, Rachid and Henzinger, Thomas A and Singh, Vasu}, journal = {Formal Methods in System Design}, number = {3}, pages = {297 -- 331}, publisher = {Springer}, title = {{Verification of STM on relaxed memory models}}, doi = {10.1007/s10703-011-0131-3}, volume = {39}, year = {2011}, } @misc{5383, abstract = {We present a new decidable logic called TREX for expressing constraints about imperative tree data structures. In particular, TREX supports a transitive closure operator that can express reachability constraints, which often appear in data structure invariants. We show that our logic is closed under weakest precondition computation, which enables its use for automated software verification. We further show that satisfiability of formulas in TREX is decidable in NP. The low complexity makes it an attractive alternative to more expensive logics such as monadic second-order logic (MSOL) over trees, which have been traditionally used for reasoning about tree data structures.}, author = {Wies, Thomas and Muñiz, Marco and Kuncak, Viktor}, issn = {2664-1690}, pages = {25}, publisher = {IST Austria}, title = {{On an efficient decision procedure for imperative tree data structures}}, doi = {10.15479/AT:IST-2011-0005}, year = {2011}, } @inproceedings{3264, abstract = {Verification of programs with procedures, multi-threaded programs, and higher-order functional programs can be effectively au- tomated using abstraction and refinement schemes that rely on spurious counterexamples for abstraction discovery. The analysis of counterexam- ples can be automated by a series of interpolation queries, or, alterna- tively, as a constraint solving query expressed by a set of recursion free Horn clauses. (A set of interpolation queries can be formulated as a single constraint over Horn clauses with linear dependency structure between the unknown relations.) In this paper we present an algorithm for solving recursion free Horn clauses over a combined theory of linear real/rational arithmetic and uninterpreted functions. Our algorithm performs resolu- tion to deal with the clausal structure and relies on partial solutions to deal with (non-local) instances of functionality axioms.}, author = {Gupta, Ashutosh and Popeea, Corneliu and Rybalchenko, Andrey}, editor = {Yang, Hongseok}, location = {Kenting, Taiwan}, pages = {188 -- 203}, publisher = {Springer}, title = {{Solving recursion-free Horn clauses over LI+UIF}}, doi = {10.1007/978-3-642-25318-8_16}, volume = {7078}, year = {2011}, } @inproceedings{3299, abstract = {We introduce propagation models, a formalism designed to support general and efficient data structures for the transient analysis of biochemical reaction networks. We give two use cases for propagation abstract data types: the uniformization method and numerical integration. We also sketch an implementation of a propagation abstract data type, which uses abstraction to approximate states.}, author = {Henzinger, Thomas A and Mateescu, Maria}, location = {Paris, France}, pages = {1 -- 3}, publisher = {Springer}, title = {{Propagation models for computing biochemical reaction networks}}, doi = {10.1145/2037509.2037510}, year = {2011}, } @inproceedings{3301, abstract = {The chemical master equation is a differential equation describing the time evolution of the probability distribution over the possible “states” of a biochemical system. The solution of this equation is of interest within the systems biology field ever since the importance of the molec- ular noise has been acknowledged. Unfortunately, most of the systems do not have analytical solutions, and numerical solutions suffer from the course of dimensionality and therefore need to be approximated. Here, we introduce the concept of tail approximation, which retrieves an approximation of the probabilities in the tail of a distribution from the total probability of the tail and its conditional expectation. This approximation method can then be used to numerically compute the solution of the chemical master equation on a subset of the state space, thus fighting the explosion of the state space, for which this problem is renowned.}, author = {Henzinger, Thomas A and Mateescu, Maria}, publisher = {Tampere International Center for Signal Processing}, title = {{Tail approximation for the chemical master equation}}, year = {2011}, } @inproceedings{3316, abstract = {In addition to being correct, a system should be robust, that is, it should behave reasonably even after receiving unexpected inputs. In this paper, we summarize two formal notions of robustness that we have introduced previously for reactive systems. One of the notions is based on assigning costs for failures on a user-provided notion of incorrect transitions in a specification. Here, we define a system to be robust if a finite number of incorrect inputs does not lead to an infinite number of incorrect outputs. We also give a more refined notion of robustness that aims to minimize the ratio of output failures to input failures. The second notion is aimed at liveness. In contrast to the previous notion, it has no concept of recovery from an error. Instead, it compares the ratio of the number of liveness constraints that the system violates to the number of liveness constraints that the environment violates.}, author = {Bloem, Roderick and Chatterjee, Krishnendu and Greimel, Karin and Henzinger, Thomas A and Jobstmann, Barbara}, booktitle = {6th IEEE International Symposium on Industrial and Embedded Systems}, location = {Vasteras, Sweden}, pages = {176 -- 185}, publisher = {IEEE}, title = {{Specification-centered robustness}}, doi = {10.1109/SIES.2011.5953660}, year = {2011}, } @inproceedings{3323, abstract = {We present a new decidable logic called TREX for expressing constraints about imperative tree data structures. In particular, TREX supports a transitive closure operator that can express reachability constraints, which often appear in data structure invariants. We show that our logic is closed under weakest precondition computation, which enables its use for automated software verification. We further show that satisfiability of formulas in TREX is decidable in NP. The low complexity makes it an attractive alternative to more expensive logics such as monadic second-order logic (MSOL) over trees, which have been traditionally used for reasoning about tree data structures.}, author = {Wies, Thomas and Muñiz, Marco and Kuncak, Viktor}, location = {Wrocław, Poland}, pages = {476 -- 491}, publisher = {Springer}, title = {{An efficient decision procedure for imperative tree data structures}}, doi = {10.1007/978-3-642-22438-6_36}, volume = {6803}, year = {2011}, } @inproceedings{3324, abstract = {Automated termination provers often use the following schema to prove that a program terminates: construct a relational abstraction of the program's transition relation and then show that the relational abstraction is well-founded. The focus of current tools has been on developing sophisticated techniques for constructing the abstractions while relying on known decidable logics (such as linear arithmetic) to express them. We believe we can significantly increase the class of programs that are amenable to automated termination proofs by identifying more expressive decidable logics for reasoning about well-founded relations. We therefore present a new decision procedure for reasoning about multiset orderings, which are among the most powerful orderings used to prove termination. We show that, using our decision procedure, one can automatically prove termination of natural abstractions of programs.}, author = {Piskac, Ruzica and Wies, Thomas}, editor = {Jhala, Ranjit and Schmidt, David}, location = {Texas, USA}, pages = {371 -- 386}, publisher = {Springer}, title = {{Decision procedures for automating termination proofs}}, doi = {10.1007/978-3-642-18275-4_26}, volume = {6538}, year = {2011}, } @inproceedings{3325, abstract = {We introduce streaming data string transducers that map input data strings to output data strings in a single left-to-right pass in linear time. Data strings are (unbounded) sequences of data values, tagged with symbols from a finite set, over a potentially infinite data do- main that supports only the operations of equality and ordering. The transducer uses a finite set of states, a finite set of variables ranging over the data domain, and a finite set of variables ranging over data strings. At every step, it can make decisions based on the next in- put symbol, updating its state, remembering the input data value in its data variables, and updating data-string variables by concatenat- ing data-string variables and new symbols formed from data vari- ables, while avoiding duplication. We establish that the problems of checking functional equivalence of two streaming transducers, and of checking whether a streaming transducer satisfies pre/post verification conditions specified by streaming acceptors over in- put/output data-strings, are in PSPACE. We identify a class of imperative and a class of functional pro- grams, manipulating lists of data items, which can be effectively translated to streaming data-string transducers. The imperative pro- grams dynamically modify a singly-linked heap by changing next- pointers of heap-nodes and by adding new nodes. The main re- striction specifies how the next-pointers can be used for traversal. We also identify an expressively equivalent fragment of functional programs that traverse a list using syntactically restricted recursive calls. Our results lead to algorithms for assertion checking and for checking functional equivalence of two programs, written possibly in different programming styles, for commonly used routines such as insert, delete, and reverse.}, author = {Alur, Rajeev and Cerny, Pavol}, location = {Texas, USA}, number = {1}, pages = {599 -- 610}, publisher = {ACM}, title = {{Streaming transducers for algorithmic verification of single pass list processing programs}}, doi = {10.1145/1926385.1926454}, volume = {46}, year = {2011}, } @inproceedings{3326, abstract = {Weighted automata map input words to numerical values. Ap- plications of weighted automata include formal verification of quantitative properties, as well as text, speech, and image processing. A weighted au- tomaton is defined with respect to a semiring. For the tropical semiring, the weight of a run is the sum of the weights of the transitions taken along the run, and the value of a word is the minimal weight of an accepting run on it. In the 90’s, Krob studied the decidability of problems on rational series defined with respect to the tropical semiring. Rational series are strongly related to weighted automata, and Krob’s results apply to them. In par- ticular, it follows from Krob’s results that the universality problem (that is, deciding whether the values of all words are below some threshold) is decidable for weighted automata defined with respect to the tropical semir- ing with domain ∪ {∞}, and that the equality problem is undecidable when the domain is ∪ {∞}. In this paper we continue the study of the borders of decidability in weighted automata, describe alternative and direct proofs of the above results, and tighten them further. Unlike the proofs of Krob, which are algebraic in their nature, our proofs stay in the terrain of state machines, and the reduction is from the halting problem of a two-counter machine. This enables us to significantly simplify Krob’s reasoning, make the un- decidability result accessible to the automata-theoretic community, and strengthen it to apply already to a very simple class of automata: all the states are accepting, there are no initial nor final weights, and all the weights on the transitions are from the set {−1, 0, 1}. The fact we work directly with the automata enables us to tighten also the decidability re- sults and to show that the universality problem for weighted automata defined with respect to the tropical semiring with domain ∪ {∞}, and in fact even with domain ≥0 ∪ {∞}, is PSPACE-complete. Our results thus draw a sharper picture about the decidability of decision problems for weighted automata, in both the front of containment vs. universality and the front of the ∪ {∞} vs. the ∪ {∞} domains.}, author = {Almagor, Shaull and Boker, Udi and Kupferman, Orna}, location = {Taipei, Taiwan}, pages = {482 -- 491}, publisher = {Springer}, title = {{What’s decidable about weighted automata}}, doi = {10.1007/978-3-642-24372-1_37}, volume = {6996}, year = {2011}, }