Decision problems for Clark-congruential languages

A common question when studying a class of context-free grammars is whether equivalence is decidable within this class. We answer this question positively for the class of Clark-congruential grammars, which are of interest to grammatical inference. We also consider the problem of checking whether a given CFG is Clark-congruential, and show that it is decidable given that the CFG is a DCFG.Comment: Version 2 incorporates revisions prompted by the comments of anonymous referees at ICGI and LearnAu

A Compositional Framework for Preference-Aware Agents

A formal description of a Cyber-Physical system should include a rigorous specification of the computational and physical components involved, as well as their interaction. Such a description, thus, lends itself to a compositional model where every module in the model specifies the behavior of a (computational or physical) component or the interaction between different components. We propose a framework based on Soft Constraint Automata that facilitates the component-wise description of such systems and includes the tools necessary to compose subsystems in a meaningful way, to yield a description of the entire system. Most importantly, Soft Constraint Automata allow the description and composition of components' preferences as well as environmental constraints in a uniform fashion. We illustrate the utility of our framework using a detailed description of a patrolling robot, while highlighting methods of composition as well as possible techniques to employ them.Comment: In Proceedings V2CPS-16, arXiv:1612.0402

An Elementary Proof of the FMP for Kleene Algebra

Kleene Algebra (KA) is a useful tool for proving that two programs are equivalent by reasoning equationally. Because it abstracts from the meaning of primitive programs, KA's equational theory is decidable, so it integrates well with interactive theorem provers. This raises the question: which equations can we (not) prove using the laws of KA? Moreover, which models of KA are complete, in the sense that they satisfy exactly the provable equations? Kozen (1994) answered these questions by characterizing KA in terms of its language model. Concretely, equivalences provable in KA are exactly those that hold for regular expressions. Pratt (1980) observed that KA is complete w.r.t. relational models, i.e., that its provable equations are those that hold for any relational interpretation. A less known result due to Palka (2005) says that finite models are complete for KA, i.e., that provable equivalences coincide with equations satisfied by all finite KAs. Phrased contrapositively, the latter is a finite model property (FMP): any unprovable equation is falsified by a finite KA. These results can be argued using Kozen's theorem, but the implication is mutual: given that KA is complete w.r.t. finite (resp. relational) models, Palka's (resp. Pratt's) arguments show that it is complete w.r.t. the language model. We embark on a study of the different complete models of KA, and the connections between them. This yields a fourth result subsuming those of Palka and Pratt, namely that KA is complete w.r.t. finite relational models. Next, we put an algebraic spin on Palka's techniques, which yield an elementary proof of the finite model property, and by extension, of Kozen's and Pratt's theorems. In contrast with earlier approaches, this proof relies not on minimality or bisimilarity of automata, but rather on representing the regular expressions involved in terms of transformation automata

Equivalence checking for weak bi-Kleene algebra

Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a fragment of pomset automata that admits a decision procedure for language equivalence. Furthermore, we prove that this fragment corresponds precisely to series-rational expressions, i.e., rational expressions with an additional operator for bounded parallelism. As a consequence, we obtain a new proof that equivalence of series-rational expressions is decidable

Learning Pomset Automata.

We extend the L⋆ algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata

Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness

Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that can distinguish between unsuccessful programs performing different actions, by omitting the so-called early termination axiom. We develop an operational (coalgebraic) and denotational (algebraic) semantics and show that they coincide. We then characterize the behaviors of GKAT expressions in this semantics, leading to a coequation that captures the covariety of automata corresponding to these behaviors. Finally, we prove that the axioms of the reduced fragment are sound and complete w.r.t. the semantics, and then build on this result to recover a semantics that is sound and complete w.r.t. the full set of axioms

Learning Pomset Automata

We extend the L* algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata

Decision problems for Clark-congruential languages

A common question when studying a class of context-free grammars (CFGs) is whether equivalence is decidable within this class. We answer this question positively for the class of Clark-congruential grammars, which are of interest to grammatical inference. We also consider the problem of checking whether a given CFG is Clark-congruential, and show that it is decidable given that the CFG is a deterministic CFG