Simulation of Two-Way Pushdown Automata Revisited

The linear-time simulation of 2-way deterministic pushdown automata (2DPDA) by the Cook and Jones constructions is revisited. Following the semantics-based approach by Jones, an interpreter is given which, when extended with random-access memory, performs a linear-time simulation of 2DPDA. The recursive interpreter works without the dump list of the original constructions, which makes Cook's insight into linear-time simulation of exponential-time automata more intuitive and the complexity argument clearer. The simulation is then extended to 2-way nondeterministic pushdown automata (2NPDA) to provide for a cubic-time recognition of context-free languages. The time required to run the final construction depends on the degree of nondeterminism. The key mechanism that enables the polynomial-time simulations is the sharing of computations by memoization.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455

Uncovering Bugs in Distributed Storage Systems during Testing (not in Production!)

Testing distributed systems is challenging due to multiple sources of nondeterminism. Conventional testing techniques, such as unit, integration and stress testing, are ineffective in preventing serious but subtle bugs from reaching production. Formal techniques, such as TLA+, can only verify high-level specifications of systems at the level of logic-based models, and fall short of checking the actual executable code. In this paper, we present a new methodology for testing distributed systems. Our approach applies advanced systematic testing techniques to thoroughly check that the executable code adheres to its high-level specifications, which significantly improves coverage of important system behaviors. Our methodology has been applied to three distributed storage systems in the Microsoft Azure cloud computing platform. In the process, numerous bugs were identified, reproduced, confirmed and fixed. These bugs required a subtle combination of concurrency and failures, making them extremely difficult to find with conventional testing techniques. An important advantage of our approach is that a bug is uncovered in a small setting and witnessed by a full system trace, which dramatically increases the productivity of debugging

Finite state verifiers with constant randomness

We give a new characterization of $\mathsf{NL}$ as the class of languages whose members have certificates that can be verified with small error in polynomial time by finite state machines that use a constant number of random bits, as opposed to its conventional description in terms of deterministic logarithmic-space verifiers. It turns out that allowing two-way interaction with the prover does not change the class of verifiable languages, and that no polynomially bounded amount of randomness is useful for constant-memory computers when used as language recognizers, or public-coin verifiers. A corollary of our main result is that the class of outcome problems corresponding to O(log n)-space bounded games of incomplete information where the universal player is allowed a constant number of moves equals NL.Comment: 17 pages. An improved versio

Towards a Uniform Theory of Effectful State Machines

Using recent developments in coalgebraic and monad-based semantics, we present a uniform study of various notions of machines, e.g. finite state machines, multi-stack machines, Turing machines, valence automata, and weighted automata. They are instances of Jacobs' notion of a T-automaton, where T is a monad. We show that the generic language semantics for T-automata correctly instantiates the usual language semantics for a number of known classes of machines/languages, including regular, context-free, recursively-enumerable and various subclasses of context free languages (e.g. deterministic and real-time ones). Moreover, our approach provides new generic techniques for studying the expressivity power of various machine-based models.Comment: final version accepted by TOC