Konstantinos Mamouras

Probabilistic NetKAT

This paper presents a new language for network programming based on a probabilistic semantics. We extend the NetKATlanguage with new primitives for expressing probabilistic behaviors and enrich the semantics from one based on deterministic functions to one based on measurable functions on sets of packet histories. We establish fundamental properties of the semantics, prove that it is a conservative extension of the deterministic semantics, show that it satisfies a number of natural equations, and develop a notion of approximation. We present case studies that show how the language can be used to model a diverse collection of scenarios drawn from real-world networks.

KAT + B!

It is known that certain program transformations require a small amount of mutable state, a feature not explicitly provided by Kleene algebra with tests (KAT). In this paper we show how to axiomatically extend KAT with this extra feature in the form of mutable tests. The extension is conservative and is formulated as a general commutative coproduct construction. We give several results on deductive completeness and complexity of the system, as well as some examples of its use.

Nominal Kleene Coalgebra

We develop the coalgebraic theory of nominal Kleene algebra, including an alternative language-theoretic semantics, a nominal extension of the Brzozowski derivative, and a bisimulation-based decision procedure for the equational theory.

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 statically scoped 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 proposed by Gabbay and Ciancia are not complete over the semantic interpretation they propose. We then identify a slightly wider class of language models over which they are sound and complete.

Kleene Algebra with Equations

We identify sufficient conditions for the construction of free language models for systems of Kleene algebra with additional equations. The construction applies to a broad class of extensions of KA and provides a uniform approach to deductive completeness.

StreamQRE: modular specification and efficient evaluation of quantitative queries over streaming data

Real-time decision making in emerging IoT applications typically relies on computing quantitative summaries of large data streams in an efficient and incremental manner. To simplify the task of programming the desired logic, we propose StreamQRE, which provides natural and high-level constructs for processing streaming data. Our language has a novel integration of linguistic constructs from two distinct programming paradigms: streaming extensions of relational query languages and quantitative extensions of regular expressions. The former allows the programmer to employ relational constructs to partition the input data by keys and to integrate data streams from different sources, while the latter can be used to exploit the logical hierarchy in the input stream for modular specifications. We first present the core language with a small set of combinators, formal semantics, and a decidable type system. We then show how to express a number of common patterns with illustrative examples. Our compilation algorithm translates the high-level query into a streaming algorithm with precise complexity bounds on per-item processing time and total memory footprint. We also show how to integrate approximation algorithms into our framework. We report on an implementation in Java, and evaluate it with respect to existing high-performance engines for processing streaming data. Our experimental evaluation shows that (1) StreamQRE allows more natural and succinct specification of queries compared to existing frameworks, (2) the throughput of our implementation is higher than comparable systems (for example, two-to-four times greater than RxJava), and (3) the approximation algorithms supported by our implementation can lead to substantial memory savings.

Synthesis of Strategies and the Hoare Logic of Angelic 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 (partial-correctness) calculi that are useful for establishing Hoare 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.

On the Hoare theory of monadic recursion schemes

The equational theory of monadic recursion schemes is known to be decidable by the result of Sénizergues on the decidability of the problem of DPDA equivalence. In order to capture some properties of the domain of computation, we augment equations with certain hypotheses. This preserves the decidability of the theory, which we call simple implicational theory. The asymptotically fastest algorithm known for deciding the equational theory, and also for deciding the simple implicational theory, has running time that is non-elementary. We therefore consider a restriction of the properties about schemes to check: instead of arbitrary equations f ≡ g between schemes, we focus on propositional Hoare assertions {p}f{q}, where f is a scheme and p, q are tests. Such Hoare assertions have a straightforward encoding as equations. We investigate the Hoare theory of monadic recursion schemes, that is, the set of valid implications whose conclusions are Hoare assertions and whose premises are of a certain simple form. We present a sound and complete Hoare-style calculus for this theory. We also show that the Hoare theory can be decided in exponential time, and that it is complete for this class.

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.

The Hoare Logic of Deterministic and Nondeterministic Monadic Recursion Schemes

The equational theory of deterministic monadic recursion schemes is known to be decidable by the result of Sénizergues on the decidability of the problem of DPDA equivalence. In order to capture some properties of the domain of computation, we augment equations with certain hypotheses. This preserves the decidability of the theory, which we call simple implicational theory. The asymptotically fastest algorithm known for deciding the equational theory, and also for deciding the simple implicational theory, has a running time that is nonelementary. We therefore consider a restriction of the properties about schemes to check: instead of arbitrary equations f ≡ g between schemes, we focus on propositional Hoare assertions {p}f{q}, where f is a scheme and p, q are tests. Such Hoare assertions have a straightforward encoding as equations. For this subclass of program properties, we can also handle nondeterminism at the syntactic and/or at the semantic level, without increasing the complexity of the theories. We investigate the Hoare theory of monadic recursion schemes, that is, the set of valid implications whose conclusions are Hoare assertions and whose premises are of a certain simple form. We present a sound and complete Hoare-style calculus for this theory. We also show that the Hoare theory can be decided in exponential time, and that it is complete for this class.