Game semantic analysis of equivalence in IMJ

Using game semantics, we investigate the problem of verifying contextual equivalences in Interface Middleweight Java (IMJ), an imperative object calculus in which program phrases are typed using interfaces. Working in the setting where data types are non-recursive and restricted to finite domains, we identify the frontier between decidability and undecidability by reference to the structure of interfaces present in typing judgments. In particular, we show how to determine the decidability status of problem instances (over a fixed type signature) by examining the position of methods inside the term type and the types of its free identifiers. Our results build upon the recent fully abstract game semantics of IMJ. Decidability is proved by translation into visibly pushdown register automata over infinite alphabets with fresh-input recognition

On Functionality of Visibly Pushdown Transducers

Visibly pushdown transducers form a subclass of pushdown transducers that (strictly) extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. In this paper, we prove that functionality is decidable in PSpace for visibly pushdown transducers. The proof is done via a pumping argument: if a word with two outputs has a sufficiently large nesting depth, there exists a nested word with two outputs whose nesting depth is strictly smaller. The proof uses technics of word combinatorics. As a consequence of decidability of functionality, we also show that equivalence of functional visibly pushdown transducers is Exptime-Complete.Comment: 20 page

Unary Pushdown Automata and Straight-Line Programs

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards

Trace Inclusion for One-Counter Nets Revisited

One-Counter nets (OCN) consist of a nondeterministic finite control and a single integer counter that cannot be fully tested for zero. They form a natural subclass of both One-Counter Automata, which allow zero-tests and Petri Nets/VASS, which allow multiple such weak counters. The trace inclusion problem has recently been shown to be undecidable for OCN. In this paper, we contrast the complexity of two natural restrictions which imply decidability. First, we show that trace inclusion between an OCN and a deterministic OCN is NL-complete, even with arbitrary binary-encoded initial counter-values as part of the input. Secondly, we show Ackermannian completeness of for the trace universality problem of nondeterministic OCN. This problem is equivalent to checking trace inclusion between a finite and a OCN-process

A First Look at Rotation in Inactive Late-Type M Dwarfs

We have examined the relationship between rotation and activity in 14 late-type (M6-M7) M dwarfs, using high resolution spectra taken at the W.M. Keck Observatory and flux-calibrated spectra from the Sloan Digital Sky Survey. Most were selected to be inactive at a spectral type where strong H-alpha emission is quite common. We used the cross-correlation technique to quantify the rotational broadening; six of the stars in our sample have vsini > 3.5 km/s. Our most significant and perplexing result is that three of these stars do not exhibit H-alpha emission, despite rotating at velocities where previous work has observed strong levels of magnetic field and stellar activity. Our results suggest that rotation and activity in late-type M dwarfs may not always be linked, and open several additional possibilities including a rotationally-dependent activity threshold, or a possible dependence on stellar parameters of the Rossby number at which magnetic/activity "saturation" takes place in fully convective stars.Comment: 8 pages, 4 figures, accepted for publication in Ap

Equivalence of Deterministic Nested Word to Word Transducers

International audienceWe study the equivalence problem of deterministic nested word to word transducers and show it to be surprisingly robust. Modulo polynomial time reductions, it can be identified with 4 equivalence problems for diverse classes of deterministic non-copying order-preserving transducers. In particular, we present polynomial time back and fourth reductions to the morphism equivalence problem on context free languages, which is known to be solvable in polynomial time

Controlled Term Rewriting

International audienceMotivated by the problem of verification of imperative tree transformation programs, we study the combination, called controlled term rewriting systems (CntTRS), of term rewriting rules with con- straints selecting the possible rewrite positions. These constraints are specified, for each rewrite rule, by a selection automaton which defines a set of positions in a term based on tree automata computations. We show that reachability is PSPACE-complete for so-called monotonic CntTRS, such that the size of every left-hand-side of every rewrite rule is larger or equal to the size of the corresponding right-hand-side, and also for the class of context-free non-collapsing CntTRS, which transform Context-Free (CF) tree language into CF tree languages. When allowing size-reducing rules, reachability becomes undecidable, even for flat CntTRS (both sides of rewrite rules are of depth at most one) when restricting to words (i.e. function symbols have arity at most one), and for ground CntTRS (rewrite rules have no variables). We also consider a restricted version of the control such that a position is selected if the sequence of symbols on the path from that position to the root of the tree belongs to a given regular language. This restriction enables decision results in the above cases