Synthesis of Strategies Using the Hoare Logic of Angelic and Demonic Nondeterminism

We study a propositional variant of Hoare logic that can be used for reasoning about programs that exhibit both angelic and demonic nondeterminism. We work in an uninterpreted setting, where the meaning of the atomic actions is specified axiomatically using hypotheses of a certain form. Our logical formalism is entirely compositional and it subsumes the non-compositional formalism of safety games on finite graphs. We present sound and complete Hoare-style calculi that are useful for establishing partial-correctness assertions, as well as for synthesizing implementations. The computational complexity of the Hoare theory of dual nondeterminism is investigated using operational models, and it is shown that the theory is complete for exponential time

Completeness and Incompleteness in Nominal Kleene Algebra

Gabbay and Ciancia (2011) presented a nominal extension of Kleene algebra as a framework for trace semantics with dynamic allocation of resources, along with a semantics consisting of nominal languages. They also provided an axiomatization that captures the behavior of the scoping operator and its interaction with the Kleene algebra operators and proved soundness over nominal languages. In this paper we show that the axioms are complete and describe the free language models

Automata-Based Stream Processing

We propose an automata-theoretic framework for modularly expressing computations on streams of data. With weighted automata as a starting point, we identify three key features that are useful for an automaton model for stream processing: expressing the regular decomposition of streams whose data items are elements of a complex type (e.g., tuple of values), allowing the hierarchical nesting of several different kinds of aggregations, and specifying modularly the parallel execution and combination of various subcomputations. The combination of these features leads to subtle efficiency considerations that concern the interaction between nondeterminism, hierarchical nesting, and parallelism. We identify a syntactic restriction where the nondeterminism is unambiguous and parallel subcomputations synchronize their outputs. For automata satisfying these restrictions, we show that there is a space- and time-efficient streaming evaluation algorithm. We also prove that when these restrictions are relaxed, the evaluation problem becomes inherently computationally expensive

Automata Theory on Sliding Windows

In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every regular language the optimal space bound is either constant, logarithmic or linear. In this paper we continue this line of research: We present natural characterizations for the constant and logarithmic space classes and establish tight relationships to the concept of language growth. We also analyze the space complexity with respect to automata size and prove almost matching lower and upper bounds. Finally, we consider the decision problem whether a language given by a DFA/NFA admits a sliding window algorithm using logarithmic/constant space

The Complexity of Social Coordination

Coordination is a challenging everyday task; just think of the last time you organized a party or a meeting involving several people. As a growing part of our social and professional life goes online, an opportunity for an improved coordination process arises. Recently, Gupta et al. proposed entangled queries as a declarative abstraction for data-driven coordination, where the difficulty of the coordination task is shifted from the user to the database. Unfortunately, evaluating entangled queries is very hard, and thus previous work considered only a restricted class of queries that satisfy safety (the coordination partners are fixed) and uniqueness (all queries need to be satisfied). In this paper we significantly extend the class of feasible entangled queries beyond uniqueness and safety. First, we show that we can simply drop uniqueness and still efficiently evaluate a set of safe entangled queries. Second, we show that as long as all users coordinate on the same set of attributes, we can give an efficient algorithm for coordination even if the set of queries does not satisfy safety. In an experimental evaluation we show that our algorithms are feasible for a wide spectrum of coordination scenarios.Comment: VLDB201

Real-time Decision Policies with Predictable Performance

As methods and tools for Cyber-Physical Systems grow in capabilities and use, one-size-fits-all solutions start to show their limitations. In particular, tools and languages for programming an algorithm or modeling a CPS that are specific to the application domain are typically more usable, and yield better performance, than general-purpose languages and tools. In the domain of cardiac arrhythmia monitoring, a small, implantable medical device continuously monitors the patient\u27s cardiac rhythm and delivers electrical therapy when needed. The algorithms executed by these devices are streaming algorithms, so they are best programmed in a streaming language that allows the programmer to reason about the incoming data stream as the basic object, rather than force her to think about lower-level details like state maintenance and minimization. Because these devices are resource-constrained, it is useful if the programming language allowed predictable performance in terms of processing runtime and energy consumption, or more general costs. StreamQRE is a declarative streaming programming language, with an efficient and portable implementation and strong theoretical guarantees. In particular, its evaluation algorithm guarantees constant cost (runtime, memory, energy) per data item, and also calculates upper bounds on the per-item cost. Such an estimate of the cost allows early exploration of the algorithmic possibilities, while maintaining a handle on worst-case performance, on the basis of which hardware can be designed and algorithms can be tuned

Synthesis of Strategies Using the Hoare Logic of Angelic and Demonic Nondeterminism

We study a propositional variant of Hoare logic that can be used for reasoning about programs that exhibit both angelic and demonic nondeterminism. We work in an uninterpreted setting, where the meaning of the atomic actions is specified axiomatically using hypotheses of a certain form. Our logical formalism is entirely compositional and it subsumes the non-compositional formalism of safety games on finite graphs. We present sound and complete Hoare-style calculi that are useful for establishing partial-correctness assertions, as well as for synthesizing implementations. The computational complexity of the Hoare theory of dual nondeterminism is investigated using operational models, and it is shown that the theory is complete for exponential time