In contrast to register automata, the emptiness problem for pushdown register automata is exptimecomplete, independent of the register storage policy used. Recently, it has been shown that for any higher order push down system h and for any regular set c of con gurations, the set prehc, is regular. Bouajjani and meyer also show that forward reachability analysis does not result in regular sets of con. Our algorithms are based on 1 representing regular potentially in. We consider pushdown timed automata ptas that are timed automata with dense clocks augmented with a pushdown stack. Pdf reachability analysis of communicating pushdown systems. Pushdown automata introduction a pushdown automaton is a way to implement a contextfree grammar in a similar way we design dfa for a regular grammar. Reachability analysis of procedural programs with a.
In 1970 steve cook, then an assistant professor in uc berkeleys math department, and my program counselor as it happened, came up with an algorithm that allowed a random access machine to acc. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification such as modelchecking for. Pushdown automata with gaporder constraints parosh aziz abdulla1, mohamed faouzi atig1, giorgio delzanno2, and andreas podelski3 1 uppsala university 2 university of genova 3 university of freiburg abstract. Symbolic backwardsreachability analysis for higherorder. Pushdown automata, pda, are a new type of computation model pdas are like nfas but have an extra component called a stack the stack provides additional memory beyond the. In addition to a finite set of control states, a pushdown. Automata for contextfree languages languageclass syntaxgrammar automata regular regularexpressions, dfa,nfa,nfa regulargrammar. When the as are done, the machine has all of them in the stack so it.
Binary reachability analysis of discrete pushdown timed automata. We consider pushdown timed automata ptas that are timed automata with dense clocks augmented with a pushdown. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification such as modelchecking for branchingtime logics, we consider the more general class of alternating pushdown systems and use alternating finitestate automata as a representation structure for sets of their configurations. The one we will use is a slight variant on the one described in sipser. In order to reason in a uniform way about analysis problems involving both existential and universal path quantification such as modelchecking for branchingtime logics, we consider the more general class of. Reachability problem for weak multipushdown automata 3 contributions. An alternative construction in symbolic reachability analysis. We represent possibly infinite sets of configurations of such systems by means of finitestate automata. Most programming languages have deterministic pdas. Find a pushdown automaton that recognizes the language aibjck and ij or ik informally the pda for this language works by first reading and pushing the as. Higherorder counter automata hoca can be either seen as a restriction of higherorder pushdown automata hopa to a unary. An alternative construction in symbolic reachability analysis of second order pushdown systems anil seth cse department, i. We will use an extension of pushdown systems, referred to as weighted pushdown systems wpds cf.
For instance, elegant and practically efficient algorithms for boundedcontext switch analysis of multipushdown systems have been recently defined based on reductions to the reachability. Pdf we apply the symbolic analysis principle to pushdown systems. Pushdown automata with gaporder constraints 3 a renamingis a mappingren. We settle the complexity of associated reachability emptiness problems. Application to modelchecking article pdf available in lecture notes in computer science december 2003 with 462 reads how we measure reads. Whereas a stack in the sense of a pushdown automaton is an. Symbolic reachability analysis of fifochannel systems with. A distributed reachability algorithm for analysis of. The language anbn cannot be accepted by a nite automaton on the other hand, lk fanbnjn kgis accepted for any given n. A pushdown automaton pda is a finite state machine which has an additional stack storage. Reachability in pushdown register automata sciencedirect.
Sipser does not allow transitions to push multiple symbols onto the stack. In this thesis, we introduce two new classes of timed pushdown automata. An introduction to hybrid automata, numerical simulation. A distributed reachability algorithm for analysis of linear hybrid automata sumit kumar jha computer science department, carnegie mellon university, pittsburgh pa 152 abstract. An introduction to hybrid automata, numerical simulation and. At each unit of time a dfsm is given a letter from its input alphabet. Since communicating finitestate automata are the most elementary instantiation of qcp, reachability is in general undecidable bz83. We represent possibly infinite sets of configurations of such systems by means of.
Reachability analysis of multithreaded software with. Pushdown automata are computational modelstheoretical computerlike machinesthat can do more than a finite state machine, but less than a turing machine. This paper presents the design of a novel distributed algorithm dira. The formal definition in our textbook is that a pda is this. We say that ren is a renaming for w if renpxq pw for all x pv.
In contrast to register automata, where differences in register storage policies gave rise to differing complexity bounds, the emptiness problem for pushdown register automata is exptimecomplete in all cases. Reachability problem for weak multi pushdown automata 3 contributions. Model of computation for deterministic pushdown automata. A configuration of a pta includes a state, dense clock values and a stack word. Jun, 2003 we consider pushdown timed automata ptas that are timed automata with dense clocks augmented with a pushdown stack. One way to do this is by analyzing a model of the system in question in order to determine if it meets a given specification. This paper presents the design of a novel distributed algorithm dira for the reachability analysis of linear hybrid automata. This approach has been used in 9, 8 to define modelchecking algorithms for push down systems and various linear and branchingtime logics, using alternating finite state automata as representation structures of sets of stack contents.
We settle the complexity of associated reachabilityemptiness problems. We study pushdown systems where control states, stack alphabet, and transition relation, instead of being finite, are firstorder definable in a fixed countablyinfinite structure. Chapter 4 pushdown automata and contextfree languages. On the other hand, the complexity of reachability over these models is still open. Zonebased reachability analysis of densetimed pushdown automata. In that case, the accelerated sequence yiio is guaranteed to converge. Hence, reachability analysis is in general only semidecidable, see e. In particular, after formally introducing pushdown automata in section 14. Then at state q 2, if we encounter input 0 and top is null, we push 0 into stack. We consider pushdown timed automata ptas that are timed automata with dense clocks augmented with a. Pushdown automata pushdown automata pda just as a dfa is a way to implement a regular expression, a pushdown automata is a way to implement a context free grammar pda equivalent in power to a cfg can choose the representation most useful to our particular problem essentially identical to a regular automata except. We also solve the global reachability problem by representing pushdown configurations with a special register automaton. Binary reachability analysis of pushdown timed automata.
Pdf reachability problem for weak multipushdown automata. Then one can apply e cient reachability analysis of pdss to solve the reachability problem of cpdss. This paper is about reachability analysis of multipushdown systems, i. Higherorder pushdown automata pda generalise pushdown automata through the use of higherorder stacks. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Recently, it has been shown that for any higher order pushdown system h and for any regular set c of con gurations, the set prehc, is regular. Note that in all examples above the automata were normed. Reachability analysis of multithreaded software with asynchronous communication ahmed bouajjani1, javier esparza2, stefan schwoon2, and jan strejcek. Pushdown automata are an extension of finite state automata. An introduction to hybrid automata, numerical simulation and reachability analysis goran frehse syde summer school,september 10,2015 univ. Reachability analysis of firstorder definable pushdown. Pushdown automata examples with explanationtheory of. Application to modelchecking article pdf available in lecture notes in computer science december 2003 with 461 reads how we measure reads.
I it is about decidability and undecidability of some reachability problem for a simple type of hybrid automata i this work is interesting and shows relations between computation, geometry and dynamics, but my current opinion is that this direction is not very applicable outside the paper industry i the second part represents my current work in. Since products are formed when processing higherorder push commands, the state space increases. Reachability analysis of dynamical systems having piecewise. Nondeterministic pushdown automata thursday, 7 february upcoming schedule now. Pushdown automata are nondeterministic finite state machines augmented with additional memory in the form of a stack, which is why the term pushdown is used, as elements are pushed down onto the stack. The reachability analysis of recursive programs that communicate asynchronously over reliable fifo channels calls for restrictions to ensure decidability. In addition to a nite set of control states, a pushdown automaton has a stack that can be manipulated with the usual push and pop operations. Equivalence of cfgs and pdas converting pdas to cfgs restricted normal form rnf to convert a pda to a cfg, it must. We consider pushdown automata with data pdad that operate on variables ranging over the set of natural numbers. Symbolic reachability analysis timed automata kronos, uppaal linear hybrid automata hytech polyhedral flowpipe approximations checkmate orthogonal polyhedra ddt. Reachability analysis of conditional pushdown systems with. We apply the symbolic analysis principle to pushdown systems. Only the nondeterministic pda defines all the cfls. The transitions a machine makes are based not only on the input and current state, but also on the stack.
The present paper complements these results by focusing on reachability analysis. Reachability analysis of communicating pushdown systems. Pushdown automata and contextfree grammars this chapter details the design of pushdown automata pda for various languages, the conversion of cfgs to pdas, and vice versa. There are many equivalent but different definitions of pdas. Pdf on nov 1, 2017, tayssir touili and others published reachability analysis of self modifying code find, read and cite all the research you need on researchgate. Pushdown automata the pda is an automaton equivalent to the cfg in languagedefining power.
We also provide a solution to the global reachability problem, based on. Jun 10, 2017 in this tutorial you will learn how to create a pushdown automata for a given context free languagegrammar pda tutorial. Control state location reachability problem given an ita, check if a particular location is reachable from the initial states this problem is decidable key idea. Ps3 will be posted before the next class and will cover material through the end of chapter 2 of the textbook and class 29 14 february.
When the as are done, the machine has all of them in the stack so it can match them with either the bs or the cs. Zonebased reachability analysis of densetimed pushdown. We apply the symbolicanalysis principle to pushdown systems. Mtpda and srta can be seen as extensions of dtpda with multipe local clocks and several new operations. Note that, the size of the resulting pushdown system is j cjj statesjsince the product automaton is deterministic, and jstatesjcan be exponetionally large. Reachability analysis of dynamical systems having piecewiseconstant derivatives. Binary reachability analysis of pushdown timed automata with. By using the pattern technique, we give a decidable characterization of the binary reachability i. We represent possi bly infinite sets of configurations of such systems by means of. We represent possibly in nite sets of con gurations of such systems by means of nitestate. Zonebased reachability analysis of densetimed pushdown automata kristiina ausmees proving that programs behave correctly is a matter of both great theoretical interest as well as practical use. In fact, decidability holds even if discrete clocks are added to the model 8. Tree automata deal with tree structures, rather than the strings of more conventional state machines the following article deals with branching tree automata, which correspond to regular languages of trees.
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