5 research outputs found
Infinite-State Energy Games
Energy games are a well-studied class of 2-player turn-based games on a
finite graph where transitions are labeled with integer vectors which represent
changes in a multidimensional resource (the energy). One player tries to keep
the cumulative changes non-negative in every component while the other tries to
frustrate this. We consider generalized energy games played on infinite game
graphs induced by pushdown automata (modelling recursion) or their subclass of
one-counter automata. Our main result is that energy games are decidable in the
case where the game graph is induced by a one-counter automaton and the energy
is one-dimensional. On the other hand, every further generalization is
undecidable: Energy games on one-counter automata with a 2-dimensional energy
are undecidable, and energy games on pushdown automata are undecidable even if
the energy is one-dimensional. Furthermore, we show that energy games and
simulation games are inter-reducible, and thus we additionally obtain several
new (un)decidability results for the problem of checking simulation preorder
between pushdown automata and vector addition systems.Comment: 11 page
Folding interpretations
We study the polyregular string-to-string functions, which are certain
functions of polynomial output size that can be described using automata and
logic. We describe a system of combinators that generates exactly these
functions. Unlike previous systems, the present system includes an iteration
mechanism, namely fold. Although unrestricted fold can define all primitive
recursive functions, we identify a type system (inspired by linear logic) that
restricts fold so that it defines exactly the polyregular functions. We also
present related systems, for quantifier-free functions as well as for linear
regular functions on both strings and trees.Comment: Author's version of a LICS 23 pape
Couverture et Terminaison dans les réseaux de Petri Récursifs
International audienceIn the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and stack automata, most of the usual property problems are solvable but using non primitive recursive algorithms, even for coverability and termination. For almost all other extended Petri nets models containing a stack the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability and termination problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get for free a more powerful model than Petri net
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science