42 research outputs found
Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace
and Nlogspace, using an algebra with a composition law based on unification.
This new bridge between unification and complexity classes is rooted in proof
theory and more specifically linear logic and geometry of interaction. We show
how to build a model of computation in the unification algebra and then, by
means of a syntactic representation of finite permutations in the algebra, we
prove that whether an observation (the algebraic counterpart of a program)
accepts a word can be decided within logarithmic space. Finally, we show that
the construction naturally corresponds to pointer machines, a convenient way of
understanding logarithmic space computation.Comment: arXiv admin note: text overlap with arXiv:1402.432
Characterizing co-NL by a group action
International audienceIn a recent paper, Girard proposes to use his recent construction of a geometry of interaction in the hyperfinite factor in an innovative way to characterize complexity classes. We begin by giving a detailed explanation of both the choices and the motivations of Girard's definitions. We then provide a complete proof that the complexity class co-NL can be characterized using this new approach. We introduce as a technical tool the non-deterministic pointer machine, a concrete model to computes algorithms
On the decidability of linear bounded periodic cyber-physical systems
Cyber-Physical Systems (CPSs) are integrations of distributed computing systems with physical processes via a networking with actuators and sensors, where feedback loops among the components allow the physical processes to affect the computations and vice versa. Although CPSs can be found in several complex and sometimes critical real-world domains, their verification and validation often relies on simulation-test systems rather then automatic methodologies to formally verify safety requirements. In this work, we prove the decidability of the reachability problem for discrete-time linear CPSs whose physical process in isolation has a periodic behavior, up to an initial transitory phase
Groups, Graphs, Languages, Automata, Games and Second-order Monadic Logic
In this paper we survey some surprising connections between group theory, the
theory of automata and formal languages, the theory of ends, infinite games of
perfect information, and monadic second-order logic