This paper expands upon existing and introduces new formulations of Bennett's logical depth. In previously published work by Jordon Moser, notions finite-state-depth pushdown-depth were examined compared. These based on finite-state transducers information lossless pushdown compressors respectively. Unfortunately a full separation between the two was not established. formulation restricting how...

The class of visibly pushdown languages has been recently defined as a subclass of context-free languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is given by a visibly pushdown language. We establish that, unlike pushdown games with pushdown winning conditio...

This contribution presents reducing variant of the deep pushdown automata. Deep pushdown automata is a new generalization of the classical pushdown automata. Basic idea of the modification consists of allowing these automata to access more deeper parts of pushdown and reducing strings to non-input symbols in the pushdown. It works similarly to bottom-up analysis simulation of context-free gramm...

We introduce and investigate blackhole pushdown automata, variants of pushdown automata, where a string can always be pushed to the pushdown, but only a given depth of the pushdown content is remembered (the rest of the pushdown content is either canceled or becomes inaccessible). We also study blackhole variants of regulated pushdown automata, where the automaton in some distinguished states c...

We introduce a new hierarchy of higher-order nested pushdown trees generalising Alur et al.’s concept of nested pushdown trees. Nested pushdown trees are useful representations of control flows in the verification of programs with recursive calls of first-order functions. Higher-order nested pushdown trees are expansions of unfoldings of graphs generated by higher-order pushdown systems. Moreov...

Pushdown systems are a model of computation equipped with one stack where only the top of the stack is inspected and modified in each step of transitions. Although this is a natural restriction, some extensions of pushdown systems require more general operations on stack: conditional pushdown systems inspect the whole stack contents and discrete timed pushdown systems increment the ages of the ...

We study the first-order model checking problem on two generalisations of pushdown graphs. The first class is the class of nested pushdown trees. The other is the class of collapsible pushdown graphs. Our main results are the following. First-order logic with reachability is uniformly decidable on nested pushdown trees. Considering first-order logic without reachability, we prove decidability i...

A pushdown game is a two player perfect information infinite game on a transition graph of a pushdown automaton. A winning condition in such a game is defined in terms of states appearing infinitely often in the play. It is shown that if there is a winning strategy in a pushdown game then there is a winning strategy realized by a pushdown automaton. An EXPTIME procedure for finding a winner in ...

Visibly pushdown automata are popular as they are closed under Boolean operations and determinization. There exist multiple notions of timed pushdown systems like recursive timed automata, densetime pushdown automata. We explore a generalization of visibly pushdown automata over infinite words with parity acceptance condition –in which stack elements have real valued time stamps–named dense-sta...